Gauge choice in Witten's energy expression

Abstract

Witten's equation\(\not D\psi = 0\) can be interpreted as a gauge fixing condition for classical supergravity. We rigorously prove the existence of asymptotically constant solutions of the more general gauge condition\(\not D\psi = A\psi\) for almost all endomorphismsA of the spin bundle. Each gives an expression for the gravitational energy similar to Witten's. These include the choice\(A = \sqrt R\), which yields the particularly elegant energy expression first noticed by Deser.