Spectral Geometry and One-loop Divergences on Manifolds with Conical Singularities

TL;DR

This paper analyzes the structure of one-loop divergences caused by conical singularities in manifolds, deriving explicit surface correction terms for heat kernel coefficients and discussing their physical implications.

Contribution

It provides explicit formulas for surface corrections to heat kernel coefficients on manifolds with conical singularities, extending previous results to more general geometries.

Findings

Explicit surface corrections to heat kernel coefficients are derived.

Surface divergences are characterized in terms of cone angle and Riemann tensor components.

Comparison with known special cases confirms the general results.

Abstract

Geometrical form of the one-loop divergences induced by conical singularities of background manifolds is studied. To this aim the heat kernel asymptotic expansion on spaces having the structure $C_{\alpha}\times \Sigma$ near singular surface $\Sigma$ is analysed. Surface corrections to standard second and third heat coefficients are obtained explicitly in terms of angle $\alpha$ of a cone $C_{\alpha}$ and components of the Riemann tensor. These results are compared to ones to be already known for some particular cases. Physical aspects of the surface divergences are shortly discussed.