Semiclassical approximation to supersymmetric quantum gravity

TL;DR

This paper develops a semiclassical approximation for supersymmetric quantum gravity, revealing that gravitino fields influence background spacetime and early universe evolution, with implications for quantum gravitational corrections.

Contribution

It introduces a Born-Oppenheimer type expansion for supersymmetric quantum gravity, incorporating gravitino dependence and deriving corrected evolution equations.

Findings

Hamilton-Jacobi equation involves gravitino fields

A local time parameter is necessary on superspace

Quantum corrections impact early universe dynamics

Abstract

We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schrodinger equation, and quantum gravitational correction terms to this Schrodinger equation. In particular, the following consequences are found: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many fingered) local time parameter has to be present on $SuperRiem \Sigma$ (the space of all possible tetrad and gravitino fields), (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early universe. The physical meaning of these equations and results, in particular the similarities to and differences from the pure bosonic case, are discussed.