Local BRST cohomology in minimal D=4, N=1 supergravity

TL;DR

This paper computes the local BRST cohomology in minimal supergravity models, classifying gauge invariant actions, anomalies, and deformations, and demonstrating the stability of gauge transformations and the non-anomalous nature of supersymmetry.

Contribution

It provides a comprehensive cohomological analysis of minimal supergravity, revealing the structure of gauge invariants, anomalies, and deformations, including the relation between old and new minimal formulations.

Findings

Most gauge invariant actions derive from superspace integrals in old minimal supergravity.

New minimal supergravity admits additional contributions not expressible via superspace integrals.

Supersymmetry is shown to be non-anomalous, and gauge transformations are highly stable.

Abstract

The local BRST cohomology is computed in old and new minimal supergravity, including the coupling to Yang-Mills gauge multiplets. This covers the determination of all gauge invariant local actions for these models, the classification of all the possible counterterms that are invariant on-shell, of all candidate gauge anomalies, and of the possible nontrivial (continuous) deformations of the standard actions and gauge transformations. Among others it is proved that in old minimal supergravity the most general gauge invariant action can indeed be constructed from well-known superspace integrals, whereas in new minimal supergravity there are only a few additional (but important) contributions which cannot be constructed in this way without further ado. Furthermore the results indicate that supersymmetry itself is not anomalous in minimal supergravity and show that the gauge transformations are extremely stable under consistent deformations of the models. There is however an unusual deformation converting new into old minimal supergravity with local R-invariance which is reminiscent of a duality transformation.