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## High Energy Physics - Theory (hep-th) updates on the arXiv.org e-print archive

Published: 2017-09-20T20:30:00-05:00

U-duality Invariant Quantum Entropy from Sums of Kloosterman Sums. (arXiv:1709.06579v1 [hep-th])

U-duality plays a special role in the study of the microscopic degrees of freedom of supersymmetric black holes. To be consistent with duality, the black hole quantum degeneracy must obey special arithmetic properties, which are non-perturbative in nature. In this work, we study these properties from a holographic point of view, establishing a connection between arithmetic properties of Kloosterman sums and quantum gravity in $\text{AdS}_2$ space. To this end, we consider the entropy of black holes that carry non-primitive charges, in both $\mathcal{N}=8$ and $\mathcal{N}=4$ four dimensional compactifications; our analysis includes all the perturbative and non-perturbative bulk quantum corrections. The key result relies on special arithmetic properties of generalized Kloosterman sums that we develop. These are a generalization of the known Selberg identity of classical Kloosterman sums. In both the $\mathcal{N}=8$ and $\mathcal{N}=4$ examples, we recover, from the bulk quantum gravity, the non-primitive answer which is a sum over the primitive degeneracies, depending non-trivially on the discrete duality invariants. In particular, for the $\mathcal{N}=4$ case we show that the quantum gravity answer reproduces the dependence on the torsion invariant $I=\text{gcd}(Q\wedge P)$, in agreement with the microscopic formulas. For the $\mathcal{N}=8$ case, we solve a puzzle related to U-duality invariance of the supergravity answer and the corresponding one-eighth BPS degeneracy.

The superradiant instability can lead to the generation of extremely dense axion clouds around rotating black holes. We show that, despite the long lifetime of the QCD axion with respect to spontaneous decay into photon pairs, stimulated decay becomes significant above a minimum axion density and leads to extremely bright lasers. The lasing threshold can be attained for axion masses $\mu \gtrsim 10^{-8}\ \mathrm{eV}$, which implies superradiant instabilities around spinning primordial BHs with mass $\lesssim 0.01M_\odot$. We further show that lasing can be quenched by Schwinger pair production, which produces a critical electron-positron plasma within the axion cloud. Lasing can nevertheless restart once annihilation lowers the plasma density sufficiently, resulting in multiple laser bursts that repeat until the black hole spins down sufficiently to quench the superradiant instability. In particular, axions with a mass $\sim 10^{-5}\ \mathrm{eV}$ and primordial black holes with mass $\sim 10^{24}$ kg, which may account for all the dark matter in the Universe, lead to millisecond-bursts in the GHz radio-frequency range, with peak luminosities $\sim 10^{42}$ erg/s, suggesting a possible link to the observed fast radio bursts.

The BPS sectors of the Skyrme model and their non-BPS extensions. (arXiv:1709.06583v1 [hep-th])

Two recently found coupled BPS submodels of the Skyrme model are further analyzed. Firstly, we provide a geometrical formulation of the submodels in terms of the eigenvalues of the strain tensor. Secondly, we study their thermodynamical properties and show that the mean-field equations of state coincide at high pressure and read $p=\bar{\rho}/3$. We also provide evidence that matter described by the first BPS submodel has some similarity with a Bose-Einstein condensate. Moreover, we show that extending these submodels to non-BPS models by including certain additional terms of the full Skyrme model does not spoil the respective ansatz, leading to ordinary differential equations for the profile of the Skyrmion, for any value of the topological charge. This allows for an almost analytical description of the properties of Skyrmions in these models. In particular, we analytically study the breaking and restoration of the BPS property. Finally, we provide an explanation of the success of the rational map ansatz.

The Toric SO(10) F-Theory Landscape. (arXiv:1709.06609v1 [hep-th])

Supergravity theories in more than four dimensions with grand unified gauge symmetries are an important intermediate step towards the ultraviolet completion of the Standard Model in string theory. Using toric geometry, we classify and analyze six-dimensional F-theory vacua with gauge group SO(10) taking into account Mordell-Weil U(1) and discrete gauge factors. We determine the full matter spectrum of these models, including charged and neutral SO(10) singlets. Based solely on the geometry, we compute all matter multiplicities and confirm the cancellation of gauge and gravitational anomalies independent of the base space. Particular emphasis is put on symmetry enhancements at the loci of matter fields and to the frequent appearance of superconformal points. They are linked to non-toric K\"ahler deformations which contribute to the counting of degrees of freedom. We compute the anomaly coefficients for these theories as well by using a base-independent blow-up procedure and superconformal matter transitions. Finally, we identify six-dimensional supergravity models which can yield the Standard Model with high-scale supersymmetry by further compactification to four dimensions in an Abelian flux background.

Neutron star mergers as a probe of modifications of general relativity with finite-range scalar forces. (arXiv:1709.06634v1 [gr-qc])

Observations of gravitational radiation from compact binary systems provide an unprecedented opportunity to test General Relativity in the strong field dynamical regime. In this paper, we investigate how future observations of gravitational radiation from binary neutron star mergers might provide constraints on finite-range forces from a universally coupled massive scalar field. Such scalar degrees of freedom are a characteristic feature of many extensions of General Relativity. For concreteness, we work in the context of metric $f(R)$ gravity, which is equivalent to General Relativity and a universally coupled scalar field with a non-linear potential whose form is fixed by the choice of $f(R)$. In theories where neutron stars (or other compact objects) obtain a significant scalar charge, the resulting attractive finite-range scalar force has implications for both the inspiral and merger phases of binary systems. We first present an analysis of the inspiral dynamics in Newtonian limit, and forecast the constraints on the mass of the scalar and charge of the compact objects for the Advanced LIGO gravitational wave observatory. We then perform a comparative study of binary neutron star mergers in General Relativity with those of a one-parameter model of $f(R)$ gravity using fully relativistic hydrodynamical simulations. These simulations elucidate the effects of the scalar on the merger and post-merger dynamics. We comment on the utility of the full waveform (inspiral, merger, post-merger) to probe different regions of parameter space for both the particular model of $f(R)$ gravity studied here and for finite-range scalar forces more generally.

Classical states, quantum field measurement. (arXiv:1709.06711v1 [quant-ph])

Manifestly Lorentz covariant representations of the algebras of the quantized electromagnetic field and of the observables of the quantized Dirac spinor field are constructed that act on Hilbert spaces that are generated using classical random fields acting on a vacuum state, allowing a comparatively classical interpretation of the states of the theory.

Dynamical deformation of 2+1 dimensional double torus universe. (arXiv:1709.06712v1 [gr-qc])

In (2+1)-dimensional pure gravity with cosmological constant, the dynamics of double torus universe with pinching parameter is investigated. Each mode of affine stretching deformation is illustrated in the context of horizontal foliation along the holomorphic quadratic differential. The formulation of the Einstein Hilbert action for the parameters of the affine stretching is developed. Then the dynamics along one holomorphic quadratic differential will be solved concretely.

Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1. (arXiv:1709.06721v1 [hep-th])

There are two covariant descriptions of massless spin-2 particles in $D=3+1$ via a symmetric rank-2 tensor: the linearized Einstein-Hilbert (LEH) theory and the Weyl plus transverse diffeomorphism (WTDIFF) invariant model. From the LEH theory one can obtain the linearized New Massive Gravity (NMG) in $D=2+1$ via Kaluza-Klein dimensional reduction followed by a dual master action. Here we show that a similar route takes us from the

WTDIFF model to a linearized scalar tensor NMG which belongs to a larger class of consistent spin-0 modifications of NMG. We also show that a traceless master action applied to a parity singlet furnishes two new spin-2 selfdual models.

Moreover, we examine the singular replacement $h_{\mu\nu} \to h_{\mu\nu} - \eta_{\mu\nu}h/D$ and prove that it leads to consistent massive spin-2 models in $D=2+1$. They include linearized versions of unimodular topologically massive gravity (TMG) and unimodular NMG. Although the free part of those unimodular theories are Weyl invariant, we do not expect any improvement in the renormalizability. Both the linearized K-term (in NMG) and the linearized gravitational Chern-Simons term (in TMG) are invariant under longitudinal reparametrizations $\delta h_{\mu\nu} = \p_{\mu}\p_{\nu}\zeta$ which is not a symmetry of the WTDIFF Einstein-Hilbert term. Therefore, we still have one degree of freedom whose propagator behaves like $1/p^2$ for large momentum.

Completeness of scattering states of the Dirac Hamiltonian with a step potential. (arXiv:1709.06725v1 [hep-th])

The completeness, together with the orthonormality, of the eigenfunctions of the Dirac Hamiltonian with a step potential is shown explicitly. These eigenfunctions describe the scattering process of a relativistic fermion off the step potential and the resolution of the identity in terms of them (completeness) is shown by explicitly summing them up, where appropriate treatments of the momentum integrations are crucial. The result would bring about a basis on which a field theoretical treatment for such a system can be developed.

On actions for (entangling) surfaces and DCFTs. (arXiv:1709.06766v1 [hep-th])

The dynamics of surfaces and interfaces describe many physical systems, including fluid membranes, entanglement entropy and the coupling of defects to quantum field theories. Based on the formulation of submanifold calculus developed by Carter, we introduce a new variational principle for (entangling) surfaces. This principle captures all diffeomorphism constraints on surface/interface actions and their associated spacetime stress tensor. The different couplings to the geometric tensors appearing in the surface action are interpreted in terms of linear response coefficients within elasticity theory. An example of a surface action with edges at the two-derivative level is studied, including both the parity-even and parity-odd sectors. Its conformally invariant counterpart restricts the type of conformal anomalies that can appear in two-dimensional submanifolds with boundaries. Analogously to hydrodynamics, it is shown that classification methods can be used to constrain the stress tensor of (entangling) surfaces at a given order in derivatives. This analysis reveals a purely geometric parity-odd contribution to the Young modulus of a thin elastic membrane. Extending this novel variational principle to BCFTs and DCFTs in curved spacetimes allows to obtain the Ward identities for diffeomorphism and Weyl transformations. In this context, we provide a formal derivation of the contact terms in the stress tensor and of the displacement operator for a broad class of actions.

Is exponential gravity a viable description for the whole cosmological history?. (arXiv:1709.06800v1 [gr-qc])

Here we analysed a particular type of F(R) gravity, the so-called exponential gravity which includes an exponential function of the Ricci scalar in the action. Such term represents a correction to the usual Hilbert-Einstein action. By using Supernovae Ia, Barionic Acoustic Oscillations, Cosmic Microwave Background and H(z) data, the free parameters of the model are well constrained. The results show that such corrections to General Relativity become important at cosmological scales and at late-times, providing an alternative to the dark energy problem. In addition, the fits do not determine any significant difference statistically with respect to the LCDM model. Finally, such model is extended to include the inflationary epoch in the same gravitational Lagrangian. As shown in the paper, the additional terms can reproduce the inflationary epoch and satisfy the constraints from Planck data.

Semiclassical spectrum for BMN string in $Sch_5\times S^5$. (arXiv:1709.06844v1 [hep-th])

We investigate the algebraic curve for string in $Sch_5\times S^5$. We compute the semiclassical spectrum for BMN string in $Sch_5\times S^5$ from the algebraic curve. We compare our results with the anomalous dimensions in $sl(2)$ sector of the null dipole deformation of $\mathcal{N} = 4$ super Yang-Mills theory.

Langevin Diffusion Coefficients Ratio in STU Model with Higher Derivative Corrections. (arXiv:1709.06846v1 [hep-th])

In this letter, we study Langevin diffusion coefficients for the five dimensional $\mathcal{N}=2$ STU model in presence of higher derivative corrections. We obtained effect of black hole charge, corresponding to the chemical potential, on the Langevin diffusion coefficients ratio. We confirm universal behavior of transverse to longitudinal ratio of coefficients.

Critical behavior and phase transition of dilaton black holes with nonlinear electrodynamics. (arXiv:1709.06875v1 [gr-qc])

In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. At first, we consider the cosmological constant and nonlinear parameter as thermodynamic quantities which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature and Gibbs free energy in an extended phase space. We complete the analogy of the nonlinear dilaton black holes with Van der Waals liquid-gas system. We work in the canonical ensemble and hence we treat the charge of the black hole as an external fixed parameter. Moreover, we calculate the critical values of temperature, volume and pressure and show they depend on dilaton coupling constant as well as nonlinear parameter. We also investigate the critical exponents and find that they are universal and independent of the dilaton and nonlinear parameters, which is an expected result. {Finally, we explore the phase transition of nonlinear dilaton black holes by studying the Gibbs free energy of the system. We find that in case of $T>T_c$, we have no phase transition. When $T=T_c$, the system admits a second order phase transition, while for $T=T_{\rm f} Majorana fermions in three dimensions and realization in critical Weyl semimetals. (arXiv:1709.06947v1 [cond-mat.mes-hall]) We present two band models for free fermion with charge conjugation symmetry in three dimensions. Without time reversal symmetry (TRS), the weak pairing gapless$A$-phase is a Majorana fermion$p_x+ip_y$wave FFLO state while the strong pairing gapped$B$-phase belongs to topologically trivial Class$D$. With TRS, there is a Majorana fermion$B$-phase belonging to Class$DIII$with a non-zero Hopf invariant. The TRS$A$-phase is also a Majorana fermion FFLO state with TRS. The surface states of the TRS$B$-phase are either a valley-momentum locked Majorana-Dirac cone or a linear-quadratic mixed cone for a specific surface. The surface states of the$A$-phase on one surface are topologically nontrivial, either having$\mathbb{Z}$or$\mathbb{Z}_2$invariant depending on whether the system is TRS or not. The edge states of that surface are gapless Majorana modes. The Majorana fermion gapless FFLO states can be realized in critical Weyl semimetals (WSM) in which dual single Weyl nodes form dipoles and are nearly annihilated. The gapped$B$-phase emerges when Weyl node dipoles are about to be created. The WSM TaAs-family, a type-II WSM series Mo$_x$W$_{1-x}$Te$_2$-family, possible WSM La/LuBi$_{1-x}$Sb$_x$Te$_3$and topological crystalline insulators Sn$_{1-x}$Pb$_x$(Te,Se) are candidates to be manipulated into these critical states based on Majorana fermion models. Asymptotic safety guaranteed in supersymmetry. (arXiv:1709.06953v1 [hep-th]) We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, R-charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the a-theorem is established. We find that supersymmetry enhances the predictivity of asymptotically safe theories. Rotating and spatially twisting Locally Rotationally Symmetric Spacetimes in f(R)-Gravity: a No-Go theorem. (arXiv:1709.06964v1 [gr-qc]) Recently, in a series of papers, we established the existence and found a general solution for the simultaneously rotating and twisting locally rotationally symmetric spacetimes in general relativity, which can model inhomogeneous and dynamic astrophysical bodies. However, these spacetimes necessarily require imperfect fluids with entropy flux. Therefore, in this paper, we investigate the existence of these spacetimes in generic f(R)-gravity models, where the entropy flux is generated purely by higher order curvature effects, while the standard matter still remains a perfect fluid. However, we transparently demonstrate here, that the symmetries of these spacetimes force the theory to be general relativity. This is a novel study that shows how the geometrical properties of a spacetime can be used to restrict the theories of gravity. Restrictions of Heterotic$G_2$Structures and Instanton Connections. (arXiv:1709.06974v1 [math.DG]) This note revisits recent results regarding the geometry and moduli of solutions of the heterotic string on manifolds$Y$with a$G_2$structure. In particular, such heterotic$G_2$systems can be rephrased in terms of a differential$\check {\cal D}$acting on a complex$\check\Omega^*(Y , {\cal Q})$, where${\cal Q}=T^*Y\oplus{\rm End}(TY)\oplus{\rm End}(V)$and$\check {\cal D}$is an appropriate projection of an exterior covariant derivative${\cal D}$which satisfies an instanton condition. The infinitesimal moduli are further parametrised by the first cohomology$H^1_{\check {\cal D}}(Y,{\cal Q})$. We proceed to restrict this system to manifolds$X$with an$SU(3)$structure corresponding to supersymmetric compactifications to four dimensional Minkowski space, often referred to as Strominger--Hull solutions. In doing so, we derive a new result: the Strominger-Hull system is equivalent to a particular holomorphic Yang-Mills covariant derivative on${\cal Q}\vert_X=T^*X\oplus{\rm End}(TX)\oplus{\rm End}(V)$. Anthropic decision theory. (arXiv:1110.6437v3 [physics.data-an] UPDATED) This paper sets out to resolve how agents ought to act in the Sleeping Beauty problem and various related anthropic (self-locating belief) problems, not through the calculation of anthropic probabilities, but through finding the correct decision to make. It creates an anthropic decision theory (ADT) that decides these problems from a small set of principles. By doing so, it demonstrates that the attitude of agents with regards to each other (selfish or altruistic) changes the decisions they reach, and that it is very important to take this into account. To illustrate ADT, it is then applied to two major anthropic problems and paradoxes, the Presumptuous Philosopher and Doomsday problems, thus resolving some issues about the probability of human extinction. Entanglement negativity, Holography and Black holes. (arXiv:1602.01147v3 [hep-th] UPDATED) Our recent holographic entanglement negativity conjecture is applied to single subsystems in$d$- dimensional conformal field theories at finite temperatures dual to bulk$AdS_{d+1}$-Schwarzschild black holes. The holographic entanglement negativity is related to the holographic mutual information and characterizes the upper bound on the distillable entanglement though the elimination of the thermal contributions. This non trivial example provides extremely strong evidence towards the universality of the conjecture. Dynamically flavored description of holographic QCD in the presence of a magnetic field. (arXiv:1604.07197v6 [hep-th] UPDATED) We construct the gravitational solution of the Witten-Sakai-Sugimoto model by introducing a magnetic field on the flavor brane. With taking into account their backreaction, we re-solve the type IIA supergravity in the presence of the magnetic field. Our calculation shows the gravitational solutions are magnetic-dependent and analytic both in the bubble (confined) and black brane (deconfined) case. We study the dual field theory at the leading order in the ratio of the number of flavors and colors, also in the Veneziano limit. Some physical properties related to the hadronic physics in an external magnetic field are discussed by using our confined backreaction solution holographically. We also investigate the thermodynamics and holographic renormalization of this model in both phases by our solution. Since the backreaction of the magnetic field is considered in our gravitational solution, it allows us to study the Hawking-Page transition with flavors and colors of this model in the presence of the magnetic field. Finally we therefore obtain the holographic phase diagram with the contributions from the flavors and the magnetic field. Our holographic phase diagram is in agreement with lattice QCD result qualitatively, which thus can be interpreted as the inhibition of confinement or chirally broken symmetry by the magnetic field. Forced Fluid Dynamics from Blackfolds in General Supergravity Backgrounds. (arXiv:1606.09644v2 [hep-th] UPDATED) We present a general treatment of the leading order dynamics of the collective modes of charged dilatonic$p$-brane solutions of (super)gravity theories in arbitrary backgrounds. To this end we employ the general strategy of the blackfold approach which is based on a long-wavelength derivative expansion around an exact or approximate solution of the (super)gravity equations of motion. The resulting collective mode equations are formulated as forced hydrodynamic equations on dynamically embedded hypersurfaces. We derive them in full generality (including all possible asymptotic fluxes and dilaton profiles) in a far-zone analysis of the (super)gravity equations and in representative examples in a near-zone analysis. An independent treatment based on the study of external couplings in hydrostatic partition functions is also presented. Special emphasis is given to the forced collective mode equations that arise in type IIA/B and eleven-dimensional supergravities, where besides the standard Lorentz force couplings our analysis reveals additional couplings to the background, including terms that arise from Chern-Simons interactions. We also present a general overview of the blackfold approach and some of the key conceptual issues that arise when applied to arbitrary backgrounds. Universal features of quantum bounce in loop quantum cosmology. (arXiv:1607.06329v4 [gr-qc] UPDATED) In this Letter, we study analytically the evolutions of the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe and its linear perturbations in the framework of {\em the dressed metric approach} in loop quantum cosmology (LQC). Assuming that the evolution of the background is dominated by the kinetic energy of the inflaton at the quantum bounce, we find that both evolutions of the background and its perturbations are independent of the inflationary potentials during the pre-inflationary phase. During this period the effective potentials of the perturbations can be well approximated by a P\"oschl-Teller (PT) potential, from which we find analytically the mode functions and then calculate the corresponding Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary model with a single scalar field. Imposing the Bunch-Davies (BD) vacuum in the contracting phase prior to the bounce when the modes are all inside the Hubble horizon, we show that particles are generically created due to the pre-inflation dynamics. Matching them to those obtained in the slow-roll inflationary phase, we investigate the effects of the pre-inflation dynamics on the scalar and tensor power spectra and find features that can be tested by current and forthcoming observations. In particular, to be consistent with the Planck 2015 data, we find that the universe must have expanded at least$141$e-folds since the bounce. On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models. (arXiv:1610.08472v3 [hep-th] UPDATED) Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higher-spin symmetries at large N. In this paper, we compute the scaling dimensions of the higher-spin operators in these models, to leading order in the 1/N expansion and exactly in the 't Hooft coupling. We obtain these results in two independent ways: by using conformal symmetry and the classical equations of motion to fix the structure of the current non-conservation, and by a direct Feynman diagram calculation. The full dependence on the 't Hooft coupling can be restored by using results that follow from the weakly broken higher-spin symmetry. This analysis also allows us to obtain some explicit results for the non-conserved, parity-breaking structures that appear in planar three-point functions of the higher-spin operators. At large spin, we find that the anomalous dimensions grow logarithmically with the spin, in agreement with general expectations. This logarithmic behavior disappears in the strong coupling limit, where the anomalous dimensions turn into those of the critical O(N) or Gross-Neveu models, in agreement with the conjectured 3d bosonization duality. Covariant holographic entanglement negativity. (arXiv:1611.00593v2 [hep-th] UPDATED) We propose a covariant holographic conjecture for the entanglement negativity of mixed states in bipartite systems described by$d$-dimensional conformal field theories dual to bulk non static$AdS_{d+1}$configurations. Application of our conjecture to$(1+1)$-dimensional conformal field theories dual to bulk rotating BTZ black holes exactly reproduces the corresponding entanglement negativity in the large central charge limit and characterizes the distillable entanglement. We further demonstrate that our conjecture applied to the case of bulk extremal rotating BTZ black holes also characterizes the entanglement negativity for the chiral half of the corresponding zero temperature$(1+1)$-dimensional holographic conformal field theories. M-theory Potential from the$G_2$Hitchin Functional in Superspace. (arXiv:1611.03098v2 [hep-th] UPDATED) We embed the component fields of eleven-dimensional supergravity into a superspace of the form$X\times Y$where$X$is the standard 4D,$N=1$superspace and$Y$is a smooth 7-manifold. The eleven-dimensional 3-form gives rise to a tensor hierarchy of superfields gauged by the diffeomorphisms of$Y$. It contains a natural candidate for a$G_2$structure on$Y$, and being a complex of superforms, defines a superspace Chern-Simons invariant. Adding to this a natural generalization of the Riemannian volume on$X\times Y$and freezing the (superspin-$\frac32$and 1) supergravity fields on$X$, we obtain an approximation to the eleven-dimensional supergravity action that suffices to compute the scalar potential. In this approximation the action is the sum of the superspace Chern-Simons term and a superspace generalization of the Hitchin functional for$Y$as a$G_2$-structure manifold. Integrating out auxiliary fields, we obtain the conditions for unbroken supersymmetry and the scalar potential. The latter reproduces the Einstein-Hilbert term on$Y$in a form due to Bryant. The non-perturbative structure of the photon and gluon propagators. (arXiv:1702.02954v2 [hep-th] UPDATED) The non-perturbative structure of the photon and gluon propagators plays an important role in governing the dynamics of quantum electrodynamics (QED) and quantum chromodynamics (QCD) respectively. Although it is often assumed that these interacting field propagators can be decomposed into longitudinal and transverse components, as for the free case, it turns out that in general this is not possible. Moreover, the non-abelian gauge symmetry of QCD permits the momentum space gluon propagator to contain additional singular terms involving derivatives of$\delta(p)$, the appearance of which is related to confinement. Despite the possibility of the failure of the transverse-longitudinal decomposition for the photon and gluon propagators, and the appearance of singular terms in the gluon propagator, the Slavnov-Taylor identity nevertheless remains preserved. Quenched equals annealed at leading order in the colored SYK model. (arXiv:1702.04228v3 [hep-th] UPDATED) We consider a colored version of the SYK model, that is we distinguish the$D$vector fermionic fields involved in the interaction by a color. We obtain the full$1/N$series of both the quenched and annealed free energies of the model and show that at leading order the two are identical. The results can be used to study systematically the$1/N$corrections to this leading order behavior. Intertwining operators among twisted modules associated to not-necessarily-commuting automorphisms. (arXiv:1702.05845v3 [math.QA] UPDATED) We introduce intertwining operators among twisted modules or twisted intertwining operators associated to not-necessarily-commuting automorphisms of a vertex operator algebra. Let$V$be a vertex operator algebra and let$g_{1}$,$g_{2}$and$g_{3}$be automorphisms of$V$. We prove that for$g_{1}$-,$g_{2}$- and$g_{3}$-twisted$V$-modules$W_{1}$,$W_{2}$and$W_{3}$, respectively, such that the vertex operator map for$W_{3}$is injective, if there exists a twisted intertwining operator of type${W_{3}\choose W_{1}W_{2}}$such that the images of its component operators span$W_{3}$, then$g_{3}=g_{1}g_{2}$. We also construct what we call the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators among twisted modules of suitable types. The proofs of these results involve careful analysis of the analytic extensions corresponding to the actions of the not-necessarily-commuting automorphisms of the vertex operator algebra. Very light dilaton and naturally light Higgs boson. (arXiv:1703.05081v3 [hep-ph] UPDATED) We study very light dilaton, arising from a scale-invariant ultraviolet theory of the Higgs sector in the standard model of particle physics. Imposing the scale symmetry below the ultraviolet scale of the Higgs sector, we alleviate the fine-tuning problem associated with the Higgs mass. When the electroweak symmetry is spontaneously broken radiatively \`a la Coleman-Weinberg, the dilaton develops a vacuum expectation value away from the origin to give an extra contribution to the Higgs potential so that the Higgs mass becomes naturally around the electroweak scale. The ultraviolet scale of the Higgs sector can be therefore much higher than the electroweak scale, as the dilaton drives the Higgs mass to the electroweak scale. We also show that the light dilaton in this scenario is a good candidate for dark matter of mass$m_D\sim 1~{\rm eV}-10~{\rm keV}$, if the ultraviolet scale is about$10-100~{\rm TeV}$. Finally we propose a dilaton-assisted composite Higgs model to realize our scenario. In addition to the light dilaton the model predicts a heavy${\rm U}(1)$axial vector boson and two massive, oppositely charged, pseudo Nambu-Goldstone bosons, which might be accessible at LHC. Mass generation by a Lorentz-invariant gas of spacetime defects. (arXiv:1703.10585v3 [hep-th] UPDATED) We present a simple model of defects embedded in flat spacetime, where the model is designed to maintain Lorentz invariance over large length scales. Even without remnant Lorentz violation, there are still effects from these spacetime defects on the propagation of physical fields, notably mass generation for scalars and Dirac fermions. Dynamics of cosmological perturbations in modified Brans-Dicke cosmology with matter-scalar field interaction. (arXiv:1704.08925v2 [gr-qc] UPDATED) In this work we focus on a novel completion of the well-known Brans-Dicke theory that introduces an interaction between the dark energy and dark matter sectors, known as complete Brans-Dicke (CBD) theory. We obtain viable cosmological accelerating solutions that fit Supernovae observations with great precision without any scalar potential$V(\phi)$. We use these solutions to explore the impact of the CBD theory on the large scale structure by studying the dynamics of its linear perturbations. We observe a growing behavior of the lensing potential$\Phi_{+}$at late-times, while the growth rate is actually suppressed relatively to$\Lambda$CDM, which allows the CBD theory to provide a competitive fit to current RSD measurements of$f\sigma_{8}$. However, we also observe that the theory exhibits a pathological change of sign in the effective gravitational constant concerning the perturbations on sub-horizon scales that could pose a challenge to its validity. Nonsingular universe in massive gravity's rainbow. (arXiv:1705.01099v3 [gr-qc] UPDATED) One of the fundamental open questions in cosmology is whether we can regard the universe evolution without singularity like a Big Bang or a Big Rip. This challenging subject stimulates one to regard a nonsingular universe in the far past with an arbitrarily large vacuum energy. Considering the high energy regime in the cosmic history, it is believed that Einstein gravity should be corrected to an effective energy dependent theory which could be acquired by gravity's rainbow. On the other hand, employing massive gravity provided us with solutions to some of the long standing fundamental problems of cosmology such as cosmological constant problem and self acceleration of the universe. Considering these aspects of gravity's rainbow and massive gravity, in this paper, we initiate studying FRW cosmology in the massive gravity's rainbow formalism. At first, we show that although massive gravity modifies the FRW cosmology, but it does not itself remove the big bang singularity. Then, we generalize the massive gravity to the case of energy dependent spacetime and find that massive gravity's rainbow can remove the early universe singularity. We bring together all the essential conditions for having a nonsingular universe and the effects of both gravity's rainbow and massive gravity generalizations on such criteria are determined. Entanglement entropy and Fisher information metric for closed bosonic strings in homogeneous plane wave background. (arXiv:1705.01873v2 [hep-th] UPDATED) We derive the extended renormalized entanglement entropy (EREE) and the Fisher information metric in the case of closed bosonic strings in homogeneous plane wave background. Our investigations are conducted within the framework of Thermo Field Dynamics (TFD). The formalism is also illustrated on the example of some particular models in condensed matter physics and the non-equilibrium case for system with dissipations. Bulk reconstruction in AdS and Gel'fand-Graev-Radon Transform. (arXiv:1705.06985v2 [hep-th] UPDATED) The bulk reconstruction formula for a Euclidean anti-de Sitter space is directly related to the inverse of the Gel'fand-Graev-Radon transform. Correlation functions of a conformal scalar field theory in the boundary are thereby related to correlation functions of a self-interacting scalar field theory in the bulk at different loop orders. Soft Hair as a Soft Wig. (arXiv:1706.00436v2 [hep-th] UPDATED) We consider large gauge transformations of gravity and electromagnetism in D=4 asymptotically flat spacetime. Already at the classical level, we identify a canonical transformation that decouples the soft variables from the hard dynamics. We find that only the soft dynamics is constrained by BMS or large U(1) charge conservation. Physically this corresponds to the fact that sufficiently long-wavelength photons or gravitons that are added to the in-state will simply pass through the interaction region; they scatter trivially in their own sector. This implies in particular that the large gauge symmetries bear no relevance to the black hole information paradox. We also present the quantum version of soft decoupling. As a consistency check, we show that the apparent mixing of soft and hard modes in the original variables arises entirely from the long range field of the hard charges, which is fixed by gauge invariance and so contains no additional information. Resonant Transmission in One-Dimensional Quantum Mechanics with Two Independent Point Interactions: Full Parameter Analysis. (arXiv:1706.01595v2 [quant-ph] UPDATED) We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by$U(2)\times U(2)$, which is described by eight real parameters. We perform an analysis of perfect resonant transmission on the whole parameter space. By investigating the effects of the two point interactions on the scattering matrix of plane wave, we find the condition under which perfect resonant transmission occurs. We also provide the physical interpretation of the resonance condition. Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics. (arXiv:1706.09833v2 [gr-qc] UPDATED) The concept of effective dynamics has proven successful in LQC, the cosmological sector of LQG. We apply the same idea in the full theory, by computing the expectation value of the scalar constraint with respect to some coherent states peaked on the phase-space variables of flat Robertson-Walker spacetime. We comment on the relation with effective LQC and find a deviation stemming from the Lorentzian part of the Hamiltonian. Quantum transfer-matrices for the sausage model. (arXiv:1706.09941v2 [hep-th] UPDATED) In this work we revisit the problem of the quantization of the two-dimensional O(3) non-linear sigma model and its one-parameter integrable deformation -- the sausage model. Our consideration is based on the so-called ODE/IQFT correspondence, a variant of the Quantum Inverse Scattering Method.The approach allowed us to explore the integrable structures underlying the quantum O(3)/sausage model. Among the obtained results is a system of non-linear integral equations for the computation of the vacuum eigenvalues of the quantum transfer-matrices. A note on NMHV form factors from the Gra{\ss}mannian and the twistor string. (arXiv:1707.00443v2 [hep-th] UPDATED) In this note we investigate Gra{\ss}mannian formulas for form factors of the chiral part of the stress-tensor multiplet in$\mathcal{N}=4$superconformal Yang-Mills theory. We present an all-$n$contour for the$G(3,n+2)$Gra{\ss}mannian integral of NMHV form factors derived from on-shell diagrams and the BCFW recursion relation. In addition, we study other$G(3,n+2)$formulas obtained from the connected prescription introduced recently. We find a recursive expression for all$n$and study its properties. For$n \geq 6$, our formula has the same recursive structure as its amplitude counterpart, making its soft behaviour manifest. Finally, we explore the connection between the two Gra{\ss}mannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes. Frame-dependence of higher-order inflationary observables in scalar-tensor theories. (arXiv:1707.00984v2 [gr-qc] UPDATED) In the context of scalar-tensor theories of gravity we compute the third-order corrected spectral indices in the slow-roll approximation. The calculation is carried out by employing the Green's function method for scalar and tensor perturbations in both the Einstein and Jordan frames. Then, using the interrelations between the Hubble slow-roll parameters in the two frames we find that the frames are equivalent up to third order. Since the Hubble slow-roll parameters are related to the potential slow-roll parameters, we express the observables in terms of the latter which are manifestly invariant. Nevertheless, the same inflaton excursion leads to different predictions in the two frames since the definition of the number of e-folds differs. To illustrate this effect we consider a nonminimal inflationary model and find that the difference in the predictions grows with the nonminimal coupling and it can actually be larger than the difference between the first and third order results for the observables. Finally, we demonstrate the effect of various end-of-inflation conditions on the observables. These effects will become important for the analyses of inflationary models in view of the improved sensitivity of future experiments. Expansion of magnetic neutron stars in an energy (in)dependent spacetime. (arXiv:1707.06460v2 [gr-qc] UPDATED) Regarding the strong magnetic field of neutron stars and high energy regime scenario which is based on high curvature region near the compact objects, one is motivated to study magnetic neutron stars in an energy dependent spacetime. In this paper, we show that such strong magnetic field and energy dependency of spacetime have considerable effects on the properties of neutron stars. We examine the variations of maximum mass and related radius, Schwarzschild radius, average density, gravitational redshift, Kretschmann scalar and Buchdahl theorem due to magnetic field and also energy dependency of metric. First, it will be shown that the maximum mass and radius of neutron stars are increasing function of magnetic field while average density, redshift, the strength of gravity and Kretschmann scalar are decreasing functions of it. These results are due to a repulsive-like force behavior for the magnetic field. Next, the effects of the gravity's rainbow will be studied and it will be shown that by increasing the rainbow function, the neutron stars could enjoy an expansion in their structures. Then, we obtain a new relation for the upper mass limit of a static spherical neutron star with uniform density in gravity's rainbow (Buchdahl limit) in which such upper limit is modified as$M_{eff}<\frac{4c^{2}R}{9G}$. In addition, stability and energy conditions for the equation of state of neutron star matter are also investigated and a comparison with empirical results is done. It is notable that the numerical study in this paper is conducted by using the lowest order constrained variational (LOCV) approach in the presence of magnetic field employing AV18 potential. Analytic integrability for strings on$ \eta $and$ \lambda $deformed backgrounds. (arXiv:1707.07172v3 [hep-th] UPDATED) In this paper, based on simple analytic techniques, we explore the integrability conditions for classical stringy configurations defined over$ \eta $as well as$ \lambda $- deformed backgrounds. We perform our analysis considering classical string motions within various subsectors of the full target space geometry. It turns out that classical string configurations defined over$ \eta $- deformed backgrounds are non-integrable whereas on the other hand, the corresponding configurations are integrable over the$ \lambda $- deformed background. Our analysis therefore imposes a strong constraint on the operator spectrum associated with the corresponding dual gauge theories at strong coupling. Generalized plane waves in Poincar\'e gauge theory of gravity. (arXiv:1708.08766v2 [gr-qc] UPDATED) A family of exact vacuum solutions, representing generalized plane waves propagating on the (anti-)de Sitter background, is constructed in the framework of Poincar\'e gauge theory. The wave dynamics is defined by the general Lagrangian that includes all parity even and parity odd invariants up to the second order in the gauge field strength. The structure of the solution shows that the wave metric significantly depends on the spacetime torsion. On the end stage of spherical gravitational collapse in a cosmological scenario. (arXiv:1709.03798v2 [gr-qc] UPDATED) We consider the end stage of spherical gravitational collapse in a cosmological setting. As an alternative to standard spherical top-hat collapse, an expanding FLRW metric is matched to a generic contracting solution of Einstein's equations on a space-like hypersurface. Using the Israel junction conditions, this is done at a time when the scale factor of expansion reaches its maximum value. In this scenario, we first show that inhomogeneous dust collapse of the LTB type are ruled out by virtue of the junction conditions. We then investigate non-dust like collapse with vanishing radial pressure, and show that this can lead to a known regular interior Schwarzschild solution, without ad hoc virialization. The other possibilities at equilibrium invariably lead to naked singularities, and we obtain a new class of such naked singularities. Finally, we consider a simplistic analytic model for collapse, and show via the matching process that it can lead to the formation of singularity-free space-times as the end stage, while respecting the known cosmological parameters. The presence of trapped surfaces in this example do not lead to singularities, due to a violation of the strong energy condition. Quantum Entanglement of the Sachdev-Ye-Kitaev Models. (arXiv:1709.06259v2 [cond-mat.str-el] UPDATED) The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical model of fermions interacting with$q$-body random couplings. For$q=2$, it describes free particles, and is non-chaotic in the many-body sense, while for$q>2$it is strongly interacting and exhibits many-body chaos. In this work we study the entanglement entropy (EE) of the SYK$q$models, for a bipartition of$N$real or complex fermions into subsystems containing$2m$real/$m$complex fermions and$N-2m$/$N-m$fermions in the remainder. For the free model SYK$2$, we obtain an analytic expression for the EE, derived from the$\beta$-Jacobi random matrix ensemble. Furthermore, we use the replica trick and path integral formalism to show that the EE is {\em maximal} for when one subsystem is small, i.e.$m\ll N$, for {\em arbitrary}$q$. We also demonstrate that the EE for the SYK4 model is noticeably smaller than the Page value when the two subsystems are comparable in size, i.e.$m/N$is$O(1)$. Finally, we explore the EE for a model with both SYK2 and SYK4 interaction and find a crossover from SYK2 (low temperature) to SYK4 (high temperature) behavior as we vary energy. Gluon momentum fraction of the nucleon from lattice QCD. (arXiv:1611.06901v2 [hep-lat] CROSS LISTED) We perform a direct calculation of the gluon momentum fraction of the nucleon using maximally twisted mass fermion ensembles with$N_f=2+1+1$flavors at a pion mass of about$370\,\mathrm{MeV}$and a lattice spacing of$a\approx 0.082\,\mathrm{fm}$and with$N_f=2$flavors at the physical pion mass and a lattice spacing of$a\approx 0.093\,\mathrm{fm}$. In the definition of the gluon operator we employ stout smearing to obtain a statistically significant result for the bare matrix elements. In addition, we perform a lattice perturbative calculation including 2 levels of stout smearing to carry out the mixing and the renormalization of the quark and gluon operators. We find, after conversion to the$\overline{\mathrm{MS}}$scheme at a scale of$2\,\mathrm{GeV}$:$\langle x\rangle^R_g {=} 0.284(23)(23)$for pion mass of about$370\,\mathrm{MeV}$and$\langle x\rangle^R_g {=} 0.283(23)(15)\$ for the physical pion mass.