Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario

TL;DR

This paper investigates the spectral geometry of Laplace-type operators on manifolds with singular surfaces, computing heat kernel coefficients relevant for quantum brane-world models.

Contribution

It provides new calculations of heat kernel coefficients for operators with transmittal boundary conditions in brane-world scenarios.

Findings

First heat kernel coefficients computed for singular surfaces

Results relate to divergences in quantum brane-world models

Conformal anomaly contributions identified

Abstract

We study the spectral geometry of an operator of Laplace type on a manifold with a singular surface. We calculate several first coefficients of the heat kernel expansion. These coefficients are responsible for divergences and conformal anomaly in quantum brane-world scenario.