Conformal Anomaly for Free Scalar Propagation on Curved Bounded Manifolds

TL;DR

This paper calculates the conformal anomaly for a free scalar field on curved manifolds with boundaries, using heat kernel methods, with implications for holography and quantum cosmology.

Contribution

It provides a novel calculation of the conformal anomaly on curved bounded manifolds using heat kernel expansion techniques.

Findings

Explicit expression for the conformal anomaly derived.

Results relevant to holography and quantum cosmology.

Methodology applicable to other curved boundary problems.

Abstract

The trace anomaly for free propagation in the context of a conformally invariant scalar field theory defined on a curved manifold of positive constant curvature with boundary is evaluated through use of an asymptotic heat kernel expansion. In addition to their direct physical significance the results are also of relevance to the holographic principle and to Quantum Cosmology.