Heat-kernel asymptotics of locally symmetric spaces of rank one and Chern-Simons invariants

Bytsenko, A. A.

doi:10.1016/s0920-5632(01)01599-7

Cited by 7 publications

(3 citation statements)

References 39 publications

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“…Covariantly constant curvature means that locally the manifold M is a symmetric space. Various approaches to the heat kernel on such manifolds are described in detail in monographs and survey articles [282,115,109]. In particular, very detailed information may be obtained for group manifolds (see, for example, [153]) and for hyperbolic spaces [110].…”

Section: "Low Energy" Expansionmentioning

confidence: 99%

Heat kernel expansion: user's manual

2003

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The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients scattered in mathematical and physical literature. We present explicit expressions for these coefficients on manifolds with and without boundaries, subject to local and non-local boundary conditions, in the presence of various types of singularities (e.g., domain walls). In each case the heat kernel coefficients are given in terms of several geometric invariants. These invariants are derived for scalar and spinor theories with various interactions, Yang-Mills fields, gravity, and open bosonic strings. We discuss the relations between the heat kernel coefficients and quantum anomalies, corresponding anomalous actions, and covariant perturbation expansions of the effective action (both "low-" and "high-energy" ones).Comment: 113 pp, to be submitted to Phys.Repts, v2: added references and corrected typo

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Section: "Low Energy" Expansionmentioning

confidence: 99%

Heat kernel expansion: user's manual

2003

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“…The Selberg zeta function and trace formula are of significant physical interest as a tool to compute spectra of kinetic operators (and thus quantum corrections) on hyperbolic quotient manifolds. A brief list of applications includes quantum chaos [5,6], quantum JT gravity [7], torsion and topological invariants [8][9][10], heat kernels and regularized one-loop determinants [11][12][13][14][15], quantum corrections to black hole entropy [16,17], quasinormal modes [15,18], and even band theory [19]. So far, the Selberg zeta function formalism has been limited to hyperbolic quotient spacetimes.…”

Section: Jhep01(2023)049mentioning

confidence: 99%

A Selberg zeta function for warped AdS3 black holes

Martin

Poddar

2023

J. High Energ. Phys.

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The Selberg zeta function and trace formula are powerful tools used to calculate kinetic operator spectra and quasinormal modes on hyperbolic quotient spacetimes. In this article, we extend this formalism to non-hyperbolic quotients by constructing a Selberg zeta function for warped AdS3 black holes. We also consider the so-called self-dual solutions, which are of interest in connection to near-horizon extremal Kerr. We establish a map between the zeta function zeroes and the quasinormal modes on warped AdS3 black hole backgrounds. In the process, we use a method involving conformal coordinates and the symmetry structure of the scalar Laplacian to construct a warped version of the hyperbolic half-space metric, which to our knowledge is new and may have interesting applications of its own, which we describe. We end by discussing several future directions for this work, such as computing 1-loop determinants (which govern quantum corrections) on the quotient spacetimes we consider, as well as adapting the formalism presented here to more generic orbifolds.

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“…Coming back to Riemannian surfaces, Efrat [28] and Koyama [42] considered the much more difficult situation of a surface (or 3 dim hyperbolic manifold) which is non compact but has finite area (volume) (see also [16,17,18,19,24,46]). We consider manifolds with constant negative sectional curvature.…”

Section: Introductionmentioning

confidence: 99%

Zeta functions and regularized determinants related to the Selberg trace formula

Momeni,

Venkov

2011

Preprint

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For a general Fuchsian group of the first kind with an arbitrary unitary representation we define zeta functions related to the contributions of the identity, hyperbolic, elliptic and parabolic conjugacy classes in Selberg's trace formula. We present Selberg's zeta function in terms of a regularized determinant of the automorphic Laplacian. We also present the zeta function for the identity contribution in terms of a regularized determinant of the Laplacian on the two dimensional sphere. We express the zeta functions for the elliptic and parabolic contributions in terms of certain regularized determinants of one dimensional Schroedinger operator for harmonic oscillator. We decompose the determinant of the automorphic Laplacian into a product of the determinants where each factor is a determinant representation of a zeta function related to Selberg's trace formula. Then we derive an identity connecting the determinants of the automorphic Laplacians on different Riemannian surfaces related to the arithmetical groups. Finally, by using the Jacquet-Langlands correspondence we connect the determinant of the automorphic Laplacian for the unit group of quaternions to the product of the determinants of the automorphic Laplacians for certain cogruence subgroups.

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Heat-kernel asymptotics of locally symmetric spaces of rank one and Chern-Simons invariants

Abstract: The asymptotic expansion of the heat kernel associated with Laplace operators is considered for general irreducible rank-one locally symmetric spaces. Invariants of the Chern-Simons theory of irreducible U (n)− flat connections on real compact hyperbolic 3-manifolds are derived.

Cited by 7 publications

References 39 publications

Heat kernel expansion: user's manual

Heat kernel expansion: user's manual

A Selberg zeta function for warped AdS3 black holes

Zeta functions and regularized determinants related to the Selberg trace formula

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