Massive 3D Supergravity

TL;DR

This work constructs the complete off-shell ${\cal N}=1$ three-dimensional supergravity theory with a cosmological term, Einstein–Hilbert action, Lorentz Chern–Simons term, and general curvature-squared invariants, all supersymmetric. It derives the full non-linear action, analyzes supersymmetric configurations (notably Minkowski and AdS vacua and supersymmetric pp-waves), and performs a thorough linearization about a supersymmetric Minkowski vacuum to identify three unitary theories: General Massive Supergravity (GMG), New Topologically Massive Supergravity (NTMSG), and Scalar Massive Supergravity (SMSG). The GMG class includes the SUSY extensions of NMG and TMG; NTMSG yields a single massive spin-2 multiplet with a spin-3/2 partner, while SMSG propagates a dynamical scalar S and two spin-1/2 fermions, all in a unitary framework. For ${\cal N}=2$, linearized GMG is extended, unifying spin-2, spin-1, and spin-3/2 sectors, and the paper discusses potential AdS/CFT implications, including central charges that match those of TMG under certain conditions and the chiral point where logarithmic modes appear.

Abstract

We construct the N=1 three-dimensional supergravity theory with cosmological, Einstein-Hilbert, Lorentz Chern-Simons, and general curvature squared terms. We determine the general supersymmetric configuration, and find a family of supersymmetric adS vacua with the supersymmetric Minkowski vacuum as a limiting case. Linearizing about the Minkowski vacuum, we find three classes of unitary theories; one is the supersymmetric extension of the recently discovered `massive 3D gravity'. Another is a `new topologically massive supergravity' (with no Einstein-Hilbert term) that propagates a single (2,3/2) helicity supermultiplet.

Figures (2)

• Figure 1: Maximally-symmetric vacua for $\sigma=-1$ and $\hat{m}^2=\tfrac{3}{4}$, the straight line representing supersymmetric vacua.
• Figure 2: Maximally-symmetric vacua for $\sigma=1$ and $\hat{m}^2=1$, the straight line representing the supersymmetric vacua; this is the same straight line as in Fig. 1, despite appearances, because of the different scales for the $\Lambda$ axes. There is also an isolated adS vacuum at $\Lambda=-{ {\frac{1}{4}} }$, $M=0$, which is not indicated.