Related papers: Complex Geodesics in the Nariai Geometry
We study two-point correlation functions of a massive free scalar field in de Sitter space using the heat kernel formalism. Focusing on two operators in conjugate static patches we derive a geodesic approximation to the two-point correlator…
The two-point function of a free massive scalar field on a fixed background can be evaluated in the large mass limit by using a semiclassical geodesic approximation. In de Sitter space, however, this poses a puzzle. Certain spacelike…
We study general correlation functions of various quantum field theories in the holographic setup. Following the holographic proposal, we investigate correlation functions via a geodesic length connecting boundary operators. We show that…
Thermal correlators in holographic CFTs on a sphere exhibit bulk-cone singularities at points connected by null geodesics in the bulk. The operator product expansion analysis of the stress-tensor sector of the correlator shows that there…
In this note we apply heat kernels to derive some localization formula in sympletcic geometry, to study moduli spaces of flat connections on a Riemann surface, to obtain the push-forward measures for certain maps between Lie groups and to…
Extremal scalar three-point correlators in the near-NHEK geometry of Kerr black holes have recently been shown to agree with the result expected from a holographically dual non-chiral two-dimensional conformal field theory. In this paper we…
We developed the functional form of the two-point correlation function under the approximation of fixed particle number density n(bar). We solved the quasi-linear partial differential equation (PDE) through the method of characteristics to…
We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large…
We prove genuinely sharp two-sided global estimates for heat kernels on all compact rank-one symmetric spaces. This generalizes the authors' recent result obtained for a Euclidean sphere of arbitrary dimension. Furthermore, similar heat…
We study correlation functions of scalar operators on the boundary of the $AdS_3$ space deformed by moving massive particles in the context of the AdS/CFT duality. To calculate two-point correlation functions we use the geodesic…
We have considered the two-point correlation of QED in worldline formalism. In position space it has been written in terms of heat kernel. This leads to introducing the $K_1$ function, which is related with the bulk-to-boundary propagator…
The main results of this article are small time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions (Theorems 1 and 2). These results are based on the geometric concepts…
Let $G$ be a noncompact semisimple Lie group equipped with a certain invariant Riemannian metric. Then, we can consider a heat kernel function on $G$ associated to the Riemannian metric. We give an explicit formula for the heat kernel when…
We calculate holographically one and two-point functions of scalar operators at finite density and/or finite temperature. In the case of finite density and zero temperature we argue that only scalar operators can have non-zero VEVs. In the…
We compute correlation functions, specifically 1-point and 2-point functions, in holographic boundary conformal field theory (BCFT) using geodesic approximation. The holographic model consists of a massive scalar field coupled to a…
Earlier in the study of the combinatorial properties of the heat kernel of Laplace operator with covariant derivative diagram technique and matrix formalism were constructed. In particular, this formalism allows you to control the…
In this survey article, we review the relation between heat kernels and path integrals. In particular, we review recent results on the approximation of the Wiener measure on compact manifold by measures on (finite-dimensional) spaces of…
Boundary correlation functions provide insight into the emergence of an effective geometry in higher spin gravity duals of O(N) or U(N) symmetric field theories. On a compact manifold, the singlet constraint leads to nontrivial dynamics at…
In this paper we study one-dimensional conformal field theory at finite temperature dual to the two-dimensional anti-de Sitter spacetime in the Rindler coordinates. We show that conformal symmetry for thermal two-point functions manifests…
Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological…