Finite Size Effects from General Covariance and Weyl Anomaly

TL;DR

This paper investigates how finite size effects in massless theories are governed by Weyl anomalies and heat kernel coefficients, linking geometric invariants to physical effects in curved and flat spacetimes.

Contribution

It establishes a universal relation between finite size effects, Weyl anomalies, and heat kernel coefficients, extending previous results to new settings and boundary conditions.

Findings

Finite size effects are determined by heat kernel coefficients.

Universal contributions relate to Weyl anomaly coefficients.

Results confirmed for massless scalars in curved spacetime with boundary.

Abstract

By exploiting the diffeomorphism invariance we relate the finite size effects of massless theories to their Weyl anomaly. We show that the universal contributions to the finite size effects are determined by certain coefficient functions in the heat kernel expansion of the related wave operators. For massless scalars confined in a $4$-dimensional curved spacetime with boundary the relevant coefficients are given -- confirming the results of Moss and Dowker and also of Branson and Gilkey. We apply the general results to theories on bounded regions in two- and four-dimensional flat space-times and determine the change of the effective action under arbitrary conformal deformations of the regions.