(Curvature)2-terms for supergravity in three dimensions

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 (eμm,ψμ,S) for N=1 and (eμm,ψμ,ψμ∗,Aμ,B,B∗) for N=2 supergravity. The S,Aμ 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 ∂μAμ for N=2. These new propagating fields form two new physical massive supermultiplets of spins (12,0) with 2×(1+1) degrees of freedom for the N=1 case, and two physical massive N=2 supermultiplets of spins (12,12,0,0) with 2×(2+2) degrees of freedom for the N=2 case.