Radiative Corrections in 2+1 Dimensional Supergravity

TL;DR

This paper investigates radiative corrections in 2+1 dimensional supergravity, demonstrating the absence of topological mass generation at one-loop level and exploring BRST invariance in related gauge theories.

Contribution

It provides the first detailed calculation of the one-loop effective action phase in 2+1 supergravity, showing it vanishes and analyzing BRST invariance in related models.

Findings

One-loop effective action phase vanishes.

No dynamical topological mass generation occurs.

BRST invariant effective actions are constructed in related models.

Abstract

Supergravity in 2+1 dimensions has a set of first class constraints that result in two Bosonic and one Fermionic gauge invariances. When one uses Faddeev-Popov quantization, these gauge invariances result in four Fermionic scalar ghosts and two Bosonic Majorana spinor ghosts. The BRST invariance of the effective Lagrangian is found. As an example of a radiative correction, we compute the phase of the one-loop effective action in the presence of a background spin connection, and show that it vanishes. This indicates that unlike a spinor coupled to a gauge field in 2 + 1 dimensions, there is no dynamical generation of a topological mass in this model. An additional example of how a BRST invariant invariant effective action can arise in a gauge theory is provided in an appendix where the BRST invariant effective action for the classical Palatini action in 1+1 dimensions is examined.