One loop divergences and anomalies from chiral superfields in supergravity

TL;DR

This paper develops a generalized heat kernel method to analyze one-loop divergences and anomalies in chiral superfields coupled to supergravity, revealing a classical ambiguity and providing manifestly supersymmetric anomaly calculations.

Contribution

It extends previous techniques to arbitrary gauge representations and supergravity backgrounds, identifying a classical ambiguity and enabling non-perturbative anomaly computations.

Findings

Identified a classical ambiguity mixing supergravity and gauge U(1) sectors.

Calculated one-loop gauge, Kahler, and reparametrization anomalies.

Provided a manifestly supersymmetric, non-perturbative anomaly expression.

Abstract

We apply the heat kernel method (using Avramidi's non-recursive technique) to the study of the effective action of chiral matter in a complex representation of an arbitrary gauge sector coupled to background U(1) supergravity. This generalizes previous methods, which restricted to 1) real representations of the gauge sector in traditional Poincar\'e supergravity or 2) vanishing supergravity background. In this new scheme, we identify a classical ambiguity in these theories which mixes the supergravity U(1) with the gauge U(1). At the quantum level, this ambiguity is maintained since the effective action changes only by a local counterterm as one shifts a U(1) factor between the supergravity and gauge sectors. An immediate application of our formalism is the calculation of the one-loop gauge, Kahler, and reparametrization anomalies of chiral matter coupled to minimal supergravity from purely chiral loops. Our approach gives an anomaly whose covariant part is both manifestly supersymmetric and non-perturbative in the Kahler potential.