Radiative corrections in 2 + 1 dimensional supergravity

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 effective action can arise in a gauge theory is provided in an appendix where the BRST effective action for the classical Palatini action in 1 + 1 dimensions is examined.

Derivation of gauge symmetries in supergravity with a cosmological constant in 2 + 1 dimensions

“…We note that in ref. [9] the BRST transformations associated with the K = 0 limit of eq. ( 22) are derived and that a demonstration is provided of how quantum effects can be computed using a regularization scheme that respects these local gauge symmetries.…”