3D Born-Infeld Gravity and Supersymmetry

TL;DR

This paper develops a ghost-free, supersymmetric, higher-derivative gravity model in three dimensions, connecting Born-Infeld gravity with supersymmetry and extending previous models with a unique invariant.

Contribution

It constructs the most general parity-even off-shell N=1 supergravity in 3D with up to six derivatives, identifying a unique supersymmetric invariant linked to Born-Infeld gravity.

Findings

Identified a unique supersymmetric invariant matching Born-Infeld gravity expansion.

Proposed a ghost-free off-shell N=1 Born-Infeld supergravity expression.

Demonstrated how truncations recover known supergravity models.

Abstract

We construct the most general parity-even higher-derivative N=1 off-shell supergravity model in three dimensions with a maximum of six derivatives. Excluding terms quadratic in the curvature tensor with two explicit derivatives and requiring the absence of ghosts in a linearized approximation around an AdS_3 background, we find that there is a unique supersymmetric invariant which we call supersymmetric `cubic extended' New Massive Gravity. The purely gravitational part of this invariant is in agreement with an earlier analysis based upon the holographic c-theorem and coincides with an expansion of Born-Infeld gravity to the required order. Our results lead us to propose an expression for the bosonic part of off-shell N=1 Born-Infeld supergravity in three dimensions that is free of ghosts. We show that different truncations of a perturbative expansion of this expression gives rise to the bosonic part of (i) Einstein supergravity; (ii) supersymmetric New Massive Gravity and (iii) supersymmetric `cubic extended' New Massive Gravity.