An Alternative Construction of the Quantum Action for Supergravity

TL;DR

This paper introduces a new method for deriving the quantum action in supergravity theories, explicitly determining ghost interactions and reconstructing auxiliary fields through a geometric BRST algebra approach.

Contribution

It presents an alternative construction of the quantum supergravity action by explicitly deriving the quartic ghost interaction and utilizing a geometric BRST algebra framework.

Findings

Explicit derivation of the quartic ghost interaction term.

Recovery of auxiliary fields and invariant extension of classical action.

Development of a geometric BRST algebra approach for supergravity.

Abstract

We develop a method to derive the on-shell invariant quantum action of the supergravity in such a way that the quartic ghost interaction term is explicity determined. First, we reinvestigate the simple supergravity in terms of a principal superfibre bundle. This gives rise to the closed geometrical BRST algebra. Therefore we determine the open BRST algebra, which realizes the invariance of the classical action. Then, given a prescription to build the full quantum action, we obtain the quantum BRST algebra. Together with the constructed quantum action this allows us to recover the auxiliary fields and the invariant extension of the classical action.