(Curvature)^2-Terms for Supergravity in Three Dimension

TL;DR

This paper explores the impact of (Curvature)^2-terms on three-dimensional N=1 and N=2 supergravity, revealing new propagating fields and massive supermultiplets, and identifying ghost-free actions involving scalar curvature squared.

Contribution

It identifies the only two invariant (Curvature)^2 actions in 3D supergravity and analyzes the emergence of new propagating fields forming massive supermultiplets.

Findings

Only scalar curvature squared actions are ghost-free.

Non-physical fields become propagating, forming massive supermultiplets.

New massive supermultiplets with specific spins are constructed.

Abstract

We investigate the effect of (Curvature)^2-terms on N=1 and N=2 supergravity in three dimensions. We use the off-shell component fields (e_\mu{}^m, \psi_\mu, S) for N=1 and (e_\mu{}^m, \psi_\mu, \psi_\mu^*, A_\mu, B, B^*) for N=2 supergravity. The S, A_\mu and B are respectively a real scalar, a real vector and a complex scalar auxiliary fields. Both for N=1 and N=2, only two invariant actions for (Curvature)^2-terms exist, while only the actions with (Scalar Curvature)^2 are free of negative energy ghosts. Interestingly, the originally non-physical graviton and gravitino fields start propagating, together with the scalar field S for the N=1 case, or the complex scalar B and the longitudinal component \partial_\mu A^\mu for N=2. These new propagating fields form two new physical massive supermultiplets of spins (1/2,0) with 2 x (1+1) degrees of freedom for the N=1 case, and two physical massive N=2 supermultiplets of spins (1/2,1/2,0,0) with 2 x (2+2) degrees of freedom for the N=2 case.