  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.

General Relativity and Quantum Cosmology;High Energy Physics - Theory