Superfield Description of a Self-Dual Supergravity a la MacDowell-Mansouri

TL;DR

This paper develops a superfield framework for self-dual supergravity inspired by MacDowell-Mansouri theory, extending the formalism to eight dimensions and emphasizing the importance of combining supersymmetric field-strengths in the Lagrangian.

Contribution

It introduces a superfield description of self-dual supergravity and extends the supersymmetric Ashtekar formalism to higher dimensions, providing new insights into supergravity theories.

Findings

Superfield description reproduces known supersymmetric Ashtekar results.

Proper combination of supersymmetric field-strengths is essential.

Extension of formalism to eight-dimensional supergravity.

Abstract

Using MacDowell-Mansouri theory, in this work, we investigate a superfield description of the self-dual supergravity a la Ashtekar. We find that in order to reproduce previous results on supersymmetric Ashtekar formalism, it is necessary to properly combine the supersymmetric field-strength in the Lagrangian. We extend our procedure to the case of supersymmetric Ashtekar formalism in eight dimensions.