Anomaly-induced vacuum effective action with torsion: covariant solution and ambiguities

TL;DR

This paper presents a covariant solution for the anomaly-induced effective action in curved spacetime with torsion, addressing ambiguities and including local and nonlocal contributions, with implications for low-energy limits.

Contribution

First formulation of a covariant anomaly-induced effective action in spacetime with torsion, clarifying ambiguities and including local total derivative terms.

Findings

Covariant solution includes local total derivative terms.

Massless fermions contribute to anomalies via multiplicative anomalies.

Nonlocal part of the action is ambiguity-free and has a low-energy limit.

Abstract

The conformal anomaly in curved spacetime with antisymmetric torsion is reconsidered, taking into account new important details. We formulate, for the first time, the covariant solution of the anomaly-induced effective action. The covariant effective action includes local terms corresponding to total derivatives in the conformal anomaly. The contribution of massless fermions to these terms is characterized by multiplicative anomaly, coming from two different choices of doubling for the spinor operator. On the other hand, the nonlocal part of anomaly-induced action is free of ambiguities and admits a low-energy limit, similar to the effective potential in the metric-scalar theory.