Gauge Theory of Gravity and Supergravity

TL;DR

This paper develops a gauge theory framework for gravity and supergravity using complex SU(2) gauge fields, deriving Einstein and supergravity equations through self-duality constraints.

Contribution

It introduces a novel gauge-theoretic formulation of gravity and supergravity based on complex SU(2) fields with quadratic action, linking self-duality to Einstein and supergravity equations.

Findings

Self-duality constraints lead to Einstein gravity equations.

Extension to N=1 and 2 super Yang-Mills yields supergravity equations.

Self-dual solutions correspond to supergravity states.

Abstract

We present a formulation of gravity in terms of a theory based on complex SU(2) gauge fields with a general coordinate invariant action functional quadratic in the field strength. Self-duality or anti-self-duality of the field strength emerges as a constraint from the equations of motion of this theory. This in turn leads to Einstein gravity equations for a dilaton and an axion conformally coupled to gravity for the self-dual constraint. The analysis has also been extended to N=1 and 2 super Yang-Mills theory of complex SU(2) gauge fields. This leads, besides other equations of motion, to self-duality/anti-self-duality of generalized supercovariant field-strengths. The self-dual case is then shown to yield as its solutions $N = 1, 2$ supergravity equations respectively.