Gauge theory of gravity and supergravity

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 to, besides other equations of motion, 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.