Related papers: The Heat Kernel on AdS_3 and its Applications

In the case of the heat equation $u_t=u_{xx}+Vu$ on the real line there are some remarkable potentials $V$ for which the asymptotic expansion of the fundamental solution becomes a finite sum and gives an exact formula. We show that a…

We analyze the spectra of general non-minimal second-order operators. To do this, we derive the local part of the trace of the second Seeley-DeWitt heat kernel coefficient for such operators in a completely model-independent way.…

We calculate the heat-kernel coefficients, up to $a_2$, for a U(1) bundle on the 4-Ball for boundary conditions which are such that the normal derivative of the field at the boundary is related to a first-order operator in boundary…

In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are able to obtain a Harnack inequality. Our abstract formulation…

Let $\Delta$ be the Laplace--Beltrami operator acting on a non-doubling manifold with two ends $\mathbb R^m \sharp \mathcal R^n$ with $m > n \ge 3$. Let $\frak{h}_t(x,y)$ be the kernels of the semigroup $e^{-t\Delta}$ generated by $\Delta$.…

We study supersymmetric gauge theories with an R-symmetry, defined on non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a supersymmetry-preserving quotient of Euclidean AdS$_3$. We compute the exact partition…

We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises certain…

Let $(X,d,\mu)$ be a $RCD^\ast(K, N)$ space with $K\in \mathbb{R}$ and $N\in [1,\infty]$. For $N\in [1,\infty)$, we derive the upper and lower bounds of the heat kernel on $(X,d,\mu)$ by applying the parabolic Harnack inequality and the…

For $d\geq 2$, we establish the existence and uniqueness of heat kernels for a large class of time-dependent second order diffusion operator with jumps, which is the sum of time-dependent of a second order elliptic differential operators…

In this paper we derive holographic wave equations for hadrons with arbitrary spin starting from an effective action in a higher-dimensional space asymptotic to anti-de Sitter (AdS) space. Our procedure takes advantage of the local tangent…

The folded spinning string in AdS3 gives us an important insight into AdS/CFT duality. Recently its one-loop energy was analyzed in the context of AdS4/CFT3 by McLoughlin and Roiban arXiv:0807.3965, by Alday, Arutyunov and Bykov…

The electromagnetic form factors of nucleons are calculated using an AdS/QCD model by considering a Dirac field coupled to a vector field in the 5-dimensional AdS space. We also calculate a gravitational or energy-momentum form factor by…

Continuing the work arXiv:1504.05991, we discuss various aspects of three dimensional quantum gravity partition function in AdS in the semi-classical limit. The partition function is holomorphic and is the one which we obtained by using the…

We propose a map for extracting the holographic meaning of the metric for a class of warped AdS_3 black strings in type IIB supergravity. Our choice of holographic data is based upon a general prescription due to Papadimitriou. With this…

A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…

This paper provides sharp Dirichlet heat kernel estimates in inner uniform domains, including bounded inner uniform domains, in the context of certain (possibly non-symmetric) bilinear forms resembling Dirichlet forms. For instance, the…

Let $X$ be a compact oriented CR manifold of dimension $2n+1$, $n \ge 1$, with a nondegenerate Levi form of constant signature $(n_-, n_+)$. Suppose that condition $Y(q)$ holds at each point of $X$, we establish the small time asymptotics…

We compute the one loop effective action for a Quantum Field Theory at finite temperature, in the presence of background gauge fields, employing the Heat-Kernel method. This method enables us to compute the thermal corrections to the Wilson…

In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with $Rc \geq -Kg$. We accomplish this extension via…

A 'holographic formula' expressing the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter(ALAdS) space has been proposed in terms of a relative functional determinant of the scalar Laplacian in the…