Anomaly candidates and invariants of D=4, N=1 supergravity theories

TL;DR

This paper systematically classifies anomaly candidates and invariant actions in various minimal and nonminimal supergravity theories, including matter couplings, using descent equations to ensure local supersymmetry consistency.

Contribution

It provides the first comprehensive analysis of anomalies and invariants in old, new, and nonminimal supergravity with matter multiplets, solving descent equations for these cases.

Findings

Complete list of anomaly candidates for minimal supergravity

Explicit forms of invariant local actions including matter couplings

Identification of potential anomalies in nonminimal supergravity

Abstract

All anomaly candidates and the form of the most general invariant local action are given for old and new minimal supergravity, including the cases where additional Yang--Mills and chiral matter multiplets are present. Furthermore nonminimal supergravity is discussed. In this case local supersymmetry itself may be anomalous and some of the corresponding anomaly candidates are given explicitly. The results are obtained by solving the descent equations which contain the consistency equation satisfied by integrands of anomalies and invariant actions.