Supergravity on a 3-torus: quantum linearization instabilities with a supergroup

TL;DR

This paper extends the study of quantum linearization stability conditions to supergravity on a 3-torus, showing that physical states are obtained via group-averaging over the supergroup of supersymmetry.

Contribution

It introduces fermionic linearization stability conditions in supergravity and demonstrates that physical states are constructed through supergroup averaging, generalizing previous results in quantum gravity.

Findings

States satisfying stability conditions are obtained by supergroup averaging.

Fermionic stability conditions are incorporated alongside bosonic ones.

The supergroup structure governs the quantum constraints in supergravity.

Abstract

It is well known that linearized gravity in spacetimes with compact Cauchy surfaces and continuous symmetries suffers from linearization instabilities: solutions to classical linearized gravity in such a spacetime must satisfy so-called linearization stability conditions (or constraints) for them to extend to solutions in the full non-linear theory. Moncrief investigated implications of these conditions in linearized quantum gravity in such background spacetimes and found that the quantum linearization stability constraints lead to the requirement that all physical states must be invariant under the symmetries generated by these constraints. He studied these constraints for linearized quantum gravity in flat spacetime with the spatial sections of toroidal topology in detail. Subsequently, his result was reproduced by the method of group-averaging. In this paper the quantum linearization stability conditions are studied for $\mathcal{N}=1$ simple supergravity in this spacetime. In addition to the linearization stability conditions corresponding to the spacetime symmetries, i.e. spacetime translations, there are also fermionic linearization stability conditions corresponding to the background supersymmetry. We construct all states satisfying these quantum linearization stability conditions, including the fermionic ones, and show that they are obtained by group-averaging over the supergroup of the global supersymmetry of this theory.