Physical states in $N = 1$ supergravity

TL;DR

This paper demonstrates that in N=1 supergravity, only two bosonic quantum states are allowed, characterized by exponential functions of the action, with specific topological and physical interpretations, and shows the theory's finiteness and absence of quantum corrections.

Contribution

It explicitly solves supersymmetry constraints to identify the only two physical bosonic states in N=1 supergravity and analyzes their properties and implications.

Findings

Only two bosonic states are allowed, of the form const.~exp~(± I / ħ)

States with finite fermions are forbidden

N=1 supergravity has no quantum ultraviolet divergences or corrections

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.