Self-dual gravity and self-dual Yang-Mills in the context of Macdowell-Mansouri formalism

TL;DR

This paper introduces a unified action for self-dual gravity and self-dual Yang-Mills within the Macdowell-Mansouri formalism, aiming to facilitate the derivation of their S-dual actions.

Contribution

It proposes a novel unified action framework for self-dual gravity and Yang-Mills theories using the Macdowell-Mansouri formalism, enabling exploration of their S-dual counterparts.

Findings

Proposed a new unified action for self-dual gravity and Yang-Mills.

Suggested a method to derive S-dual actions from the unified framework.

Potential implications for understanding dualities in gauge and gravity theories.

Abstract

In this work we propose an action which unifies self-dual gravity and self-dual Yang-Mills in the context of the Macdowell-Mansouri formalism. We claim that such an action may be used to find the S-dual action for both self-dual gravity and self-dual Yang-Mills.