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. 1997 Academic Press 1. INTRODUCTION 1.1. Topics and motivation
This paper presents the first exhaustive analysis of the local BRST cohomology in supergravity. More precisely we will analyze the two most popular formulations of four dimensional N=1 supergravity known as old [1] and new [2] minimal supergravity, including their coupling to Yang Mills gauge multiplets. The inclusion of further (matter) multiplets will be briefly discussed too.
To begin with, let me recall some general features of the local BRST cohomology. By this I mean the cohomology of the BRST operator 1 in the space of local functionals of the fields and antifields. It allows to analyze various physically relevant aspects of gauge theories in a unified framework. Historically it was above all the anomaly problem that initiated the interest in this cohomology when it became article no. PH975709 253 0003-4916Γ97 25.00