Conformal Anomalies for Interacting Scalar Fields on Curved Manifolds with Boundary

TL;DR

This paper computes the conformal anomaly for interacting scalar fields on curved manifolds with boundary, advancing the calculation to fourth-loop order through perturbative and renormalization-group methods.

Contribution

It provides explicit calculations of the conformal anomaly up to fourth-loop order for interacting scalar fields on curved manifolds with boundary, including new third and fourth-order results.

Findings

Explicit second-order contributions to the anomaly from free and interacting scalars.

Third-order anomaly contributions derived using renormalization-group techniques.

Complete fourth-loop order anomaly calculations achieved.

Abstract

The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit calculations are given for those contributions to the conformal anomaly which emerge as a result of free scalar propagation as well as from scalar self-interactions up to second order in the scalar self-coupling. The renormalisation-group behaviour of the theory is, subsequently, exploited in order to advance the evaluation of the conformal anomaly to third order in the scalar self-coupling. In effect, complete contributions to the theory's conformal anomaly are evaluated up to fourth-loop order.