Comments on SUSY Exact Action in 3D Supergravity

TL;DR

This paper investigates off-shell 3D N=1 supergravity, demonstrating that certain supersymmetric invariants can be expressed as local exact terms, with mass parameters linked to the cosmological constant.

Contribution

It shows that specific $R^2$ supersymmetric invariants in 3D supergravity are exact terms up to mass contributions related to the cosmological constant.

Findings

Supersymmetric invariants are expressed as local exact terms.

Mass parameters are proportional to the off-shell cosmological constant.

The invariants include $R^2$ and $R^2_{}$ terms.

Abstract

We consider 2+1 dimensional off-shell N = 1 pure supergravity that is constructed from graviton, gravitino and auxiliary field. We show that the $R^2$ supersymmetric invariant and $R^2_{\mu \nu}$ supersymmetric invariant are expressed as local supersymmetric exact terms up to mass terms for gravitino. In both cases, the mass parameter is proportional to the off-shell supersymmetric cosmological constant.