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~$(\pm I/\hslash )$, 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~$(-I/\hslash )$ is the wormhole ground state, and the state const.~exp~$(I/\hslash )$ is the Hartle--Hawking state. $N=1$ supergravity has no quantum ultraviolet divergences, and no quantum corrections.

9 pages, DAMTP Preprint DAMTP-R-93-4

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