Abstract
We present a formulation of gravity in terms of a theory based on complex 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 and 2 super Yang-Mills theory of complex 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 , 2 supergravity equations, respectively.
- Received 17 January 2006
DOI:https://doi.org/10.1103/PhysRevD.73.065027
©2006 American Physical Society