High Energy Physics Theory

In d-dimensional CFTs with a large number of degrees of freedom an important set of operators consists of the stress tensor and its products, multi stress tensors. Thermalization of such operators, the equality between their expectation values in heavy states and at finite temperature, is equivalent to a universal behavior of their OPE coefficients with a pair of identical heavy operators. We verify this behavior in a number of examples which include holographic and free CFTs and provide a bootstrap argument for the general case. In a free CFT we check the thermalization of multi stress tensor operators directly and also confirm the equality between the contributions of multi stress tensors to heavy-heavy-light-light correlators and to the corresponding thermal light-light two-point functions by disentangling the contributions of other light operators. Unlike multi stress tensors, these light operators violate the Eigenstate Thermalization Hypothesis and do not thermalize.

Recently, black hole symmetries have been studied widely and it has been speculated that this procedure will lead to the deeper understanding of the black hole physics. Spontaneous symmetry breaking of the horizon symmetries is one of the very recent attempt to clarify black hole thermal physics. In this work, we are going to investigate the same in three dimensional massive gravity, including higher order of Riemann tensor. We observe that the idea also works well in this gravitational theory, thereby providing stronger demand of the viability of this idea.

In this paper, we study 5dN=1Sp(N)gauge theory withNf(??N+3)flavors based on 5-brane web diagram withO5-plane. On the one hand, we discuss Seiberg-Witten curve based on the dual graph of the 5-brane web withO5-plane. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism withO5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the dual graph of the 5-brane web withO5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-type singularities.

We have calculated the thermal partition function for the thermodynamical system of massless free bosonic higher spin fields (Fronsdal theory) by using Feynman path integral formalism. However, we have established a connection between the microscopic world (Quantum statistical) of the thermodynamical system of massless free bosonic HS fields to the thermodynamics of the macroscopic world its and also we have observed the duality between the thermodynamical system of massless free HS fields ond-dimensional Minkowski spacetime and thermodynamical system of Klein-Gordon scalar fields on 4-dimensional Minkowski spacetime at the thermal equilibrium condition. The average energy of the canonical ensemble of the thermodynamical system of massless free bosonic HS fields is not in agreement with the equipartition theorem, hence it deviates from the classical behaviour of the system and it shows that the true signature of the quantum thermodynamical system.

We study the thermodynamics of ad-dimensional Schwarzschild black hole in the canonical ensemble. This generalizes York's formalism to any numberdof dimensions. The canonical ensemble, characterized by a cavity of fixed radiusrand fixed temperatureTat the boundary, allows for two possible solutions in thermal equilibrium, a small and a large black hole. From the Euclidean action and the path integral approach, we obtain the free energy, the thermodynamic energy, the pressure, and the entropy, of the black hole plus cavity system. The entropy is given by the Bekenstein-Hawking area law. The heat capacity shows that the smaller black hole is in unstable equilibrium and the larger is stable. The photon sphere radius divides the stability criterion. To study perturbations, a generalized free energy function is obtained that allows to understand the possible phase transitions between classical hot flat space and the black holes. The Buchdahl radius, that appears naturally in the general relativistic study of star structure, also shows up in our context, the free energy is zero when the cavity's radius has the Buchdahl radius value. Then, if the cavity's radius is smaller than the Buchdahl radius classical hot flat space can nucleate a black hole. It is also pointed out the link between the canonical analysis performed and the direct perturbation of the path integral. Since gravitational hot flat space is a quantum system made purely of gravitons it is of interest to compare the free energies of quantum hot flat space and the stable black hole to find for which ranges ofrandTone phase predominates over the other. Phase diagrams are displayed. The density of states at a given energy is found. Further calculations and comments are carried out, notably, a connection to thin shells indspacetime dimensions which are systems that are also apt to rigorous thermodynamics.

In this paper, we explore the five-dimensional f(T,B) teleparallel modified gravity with f_1(T,B)=T+k_1B^{n_1} and f_2(T,B)=B+k_2T^{n_2} in the brane scenario. Asymptotically, the bulk geometry converges to an AdS_5 spacetime whose cosmological constant is produced by parameters that control torsion and boundary term. The analysis of the energy density condition reveals a splitting brane process satisfying the weak and strong energy conditions for some values of the parameters n_{1,2} and k_{1,2}. In addition, we investigate the behavior of the gravitational perturbations in this scenario. In the bulk, the torsion keeps a gapless non-localizable, and stable tower of massive modes. Inside the brane core, the torsion produces new barriers and potential wells, leading to small amplitude massive modes and a massless mode localized for some values of the parameters n_{1,2} and k_{1,2}.

In this article we construct the effective field theory associated to theR?S3sector of the three-parameter deformation ofAdS3?S3?T4in the Landau-Lifshitz approximation. We use this action to compute the dispersion relation of excitations around the BMN vacuum and the perturbativeS-matrix associated to them. We are able to compute and sum all the different loop contributions to theS-matrix in this limit.

We show that a particular noncommutative geometry, sometimes called angular or?-Minkowski, requires that the spectrum of time be discrete. In this noncommutative space the time variable is not commuting with the angular variable in cylindrical coordinates. The possible values that the variable can take go from minus infinity to plus infinity, equally spaced by the scale of noncommmutativity. Possible self-adjoint extensions of the "time operator" are discussed. They give that a measurement of time can be any real value, but time intervals are still quantized.

We employ holographic techniques to explore the effects of momentum dissipation on the formation of topological defects during the critical dynamics of a strongly coupled superconductor after a linear quench of temperature. The gravity dual is the dRGT massive gravity in which the conservation of momentum in the boundary field theory is broken by the presence of a bulk graviton mass. From the scaling relations of defects number and "freeze-out" time to the quench rate for various graviton masses, we demonstrate that the momentum dissipation induced by graviton mass has little effect on the scaling laws compared to the Kibble-Zurek mechanism. Inspired from Pippard's formula in condensed matter, we propose an analytic relation between the coherence length and the graviton mass, which agrees well with the numerical results from the quasi-normal modes analysis. As a result, the coherence length decreases with respect to the graviton mass, which indicates that the momentum dissipation will augment the number of topological defects.

We construct a (1+1)dtopological field theory (TFT) whose topological defect lines (TDLs) realize the transparent HaagerupH3fusion category. This TFT has six vacua, and each of the three non-invertible simple TDLs hosts three defect operators, giving rise to a total of 15 point-like operators. The TFT data, including the three-point coefficients and lasso diagrams, are determined by solving all the sphere four-point crossing equations and torus one-point modular invariance equations. We further verify that the Cardy states furnish a non-negative integer matrix representation under TDL fusion. While many of the constraints we derive are not limited to the this particular TFT with six vacua, we leave open the construction of TFTs with two or four vacua. Finally, TFTs realizing the HaagerupH1andH2fusion categories can be obtained by gauging algebra objects. This note makes a modest offering in our pursuit of exotica and the quest for their eventual conformity.