相关论文: The Heat Kernel on AdS_3 and its Applications

In the AdS$_3$/CFT$_2$ framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems,…

This paper is an overview on our recent results in the calculation of the heat kernel in quantum field theory and quantum gravity. We introduce a deformation of the background fields (including the metric of a curved spacetime manifold) and…

Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector…

The Virasoro algebra determines all `graviton' matrix elements in AdS$_3$/CFT$_2$. We study the explicit exchange of any number of Virasoro gravitons between heavy and light CFT$_2$ operators at large central charge. These graviton…

We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered - one…

This paper studies the empirical measures of eigenvalues and singular values for random matrices drawn from the heat kernel measures on the unitary groups $\mathbb{U}_N$ and the general linear groups $\mathbb{GL}_N$, for $N\in\mathbb{N}$.…

There has been renewed interest in the path-integral computation of the partition function of AdS3 gravity, both in the metric and Chern-Simons formulations. The one-loop partition function around Euclidean AdS3 turns out to be given by the…

We extend the results of arXiv:1401.7016, computing one loop partition functions for massive fields with spin half in AdS_2 using the quasinormal mode method proposed by Denef, Hartnoll, and Sachdev in arXiv:0908.2657. We find the finite…

In the AdS/CFT correspondence, single trace operators of large-$N$ gauge theories at large spin $J$ can be described by classical spinning strings, giving a geometric and classical description of their spectrum at strong coupling. We…

It was shown by Brown and Henneaux that the classical theory of gravity on AdS_3 has an infinite-dimensional symmetry group forming a Virasoro algebra. More recently, Giveon, Kutasov and Seiberg (GKS) constructed the corresponding Virasoro…

We study the geometry of $T\bar{T}$-deformed BTZ black hole and find it can be regarded as a quotient of hyperbolic space. We then consider the massive scalar field propagating in the $T\bar{T}$-deformed BTZ black hole background. The…

The heat kernel transform H_t for the Heisenberg group is studied in detail. The main result shows that the image of H_t is a direct sum of two weighted Bergman spaces whose associated weighted functions are of oscillatory nature, i.e.…

We first study the problem of the one-loop partition function for a free massive quantum field theory living on a fixed background hyperbolic space on the field of real numbers, $\mathbb{H}^n(\mathbb{R}), \,\, n\geq 2$. Earlier attempts…

In previous works, we used a so-called deformation formula in order to study, in particular, the Borel summability of the heat kernel of some operators. A goal of this paper is to collect miscellaneous remarks related to these works. Here…

In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ \Delta^{\alpha/2}_v + v \cdot \nabla_x, \quad \alpha \in (0, 2),\ (x,v)\in {\mathbb…

The calculation of heat-kernel coefficients with the classical DeWitt algorithm has been discussed. We present the explicit form of the coefficients up to $h_5$ in the general case and up to $h_7^{min}$ for the minimal parts. The results…

In the presented paper we tackle the problem of the effective field theory in curved spacetime (cEFT) construction. To this end, we propose to use the heat kernel method. After introducing the general formalism based on the well established…

The fundamental solution of the heat equation on $R^n$ is known as the heat kernel which is also the transition density of a Brownian motion. Similar statements hold when $\R^n$ is replaced by a Lie group. We briefly demonstrate how the…

We study the one-loop effective action of certain classical type IIA string configurations in $AdS_4\times \mathbb{CP}^3$. These configurations are dual to Wilson loops in the $\mathcal{N}= 6\:$ $U(N)_k \times U(N)_{-k}$ Chern-Simons theory…

In this paper we study a new class of holographic heat engines via charged AdS black hole solutions of Einstein gravity coupled with logarithmic nonlinear $U(1)$ gauge theory. So, Logarithmic $U(1)$ AdS black holes with a horizon of…