Weyl transformations and trace anomalies in N=1, D=4 supergravities

TL;DR

This paper explores supersymmetric extensions of Weyl transformations in various N=1 supergravities in 4D, revealing the structure of trace anomalies and their relation to known geometric densities.

Contribution

It identifies supersymmetric Weyl transformations across different supergravity formulations and classifies the associated trace anomalies in these theories.

Findings

Only two types of trace anomalies exist in nonminimal and new minimal supergravities.

Trace anomalies correspond to squared Weyl density and Euler density in component form.

New minimal supergravity has additional cocycles mapped to zero in minimal supergravity.

Abstract

We identify the supersymmetric extension of Weyl transformations in various types of supergravities, the minimal, nonminimal and new minimal N=1 SUGRA in 4D, formulated in terms of superfields. Based also on previous results we conclude that there are only two types of trace anomalies in nonminimal and new minimal supergravities, which correspond to the two nontrivial cocycles of the minimal supergravity and, when reduced to component form, to the well-known squared Weyl density and Euler density. There are nevertheless in new minimal supergravity other nontrivial cocycles which, however, are mapped to zero in the minimal supergravity.