Chiral supergravity and anomalies

TL;DR

This paper explores a chiral reformulation of N=1 supergravity using a Chern-Simons approach, leading to a natural decomposition of fields and insights into axial and chiral anomalies.

Contribution

It introduces a novel chiral reformulation of supergravity based on a Chern-Simons generating function, with a natural splitting of fields and analysis of anomalies.

Findings

Decomposition of gravitational fields into selfdual and antiselfdual modes.

Splitting of Rarita-Schwinger fields into chiral components.

Analysis of implications for axial and chiral anomalies.

Abstract

Similarily as in the Ashtekar approach, the translational Chern-Simons term is, as a generating function, instrumental for a chiral reformulation of simple (N=1) supergravity. After applying the algebraic Cartan relation between spin and torsion, the resulting canonical transformation induces not only decomposition of the gravitational fields into selfdual and antiselfdual modes, but also a splitting of the Rarita-Schwinger fields into their chiral parts in a natural way. In some detail, we also analyze the consequences for axial and chiral anomalies.