Physical states in $N = 1$ supergravity

Abstract

By solving the supersymmetry constraints for physical wave-functions, it is shown that the only two allowed bosonic states in $ N = 1 $ supergravity are of the form const.~exp~$(\pm I / \hbar) $, where $ I $ is an action functional of the three-metric. States containing a finite number of fermions are forbidden. In the case that the spatial topology is $ S^3 $, the state const.~exp~$(- I / \hbar)$ is the wormhole ground state, and the state const.~exp~$(I / \hbar)$ is the Hartle--Hawking state. $ N = 1 $ supergravity has no quantum ultraviolet divergences, and no quantum corrections.