Trace anomaly and induced action for a metric-scalar background

TL;DR

This paper explores the conformal anomaly and anomaly-induced effective action in a metric-scalar background, linking low-energy induced actions to renormalization group and effective potential, and addressing ambiguities in anomaly classification.

Contribution

It extends the classification of anomalous terms to scalar backgrounds and discusses covariant forms of the induced action with regularization ambiguities.

Findings

Connection between induced action and renormalization group

Extended classification of anomalies to scalar backgrounds

Analysis of ambiguities in anomaly total derivative terms

Abstract

The conformal anomaly and anomaly-induced effective action represent useful and economic ways to describe semiclassical contributions to the action of gravity. We discuss the anomaly in the case when the background is formed by metric and scalar fields and formulate the induced action in two standard covariant forms. The analysis of induced action at low energies reveals existing connection to the renormalization group and effective potential. The classification of anomalous terms is extended to the scalar background and ambiguities in the total derivative terms in the anomaly are considered using Pauli-Villars regularization.