Massive N=2 Supergravity in Three Dimensions

TL;DR

This paper constructs off-shell invariants for two types of ${ m N}=2$ supergravity in three dimensions, analyzes their vacuum solutions, and identifies conditions for ghost-free massive modes, highlighting differences between the two theories.

Contribution

It provides explicit off-shell invariants for ${ m N}=(1,1)$ and ${ m N}=(2,0)$ supergravities and explores their vacuum solutions and physical spectra.

Findings

${ m N}=(1,1)$ invariants admit anti-de Sitter vacua with ghost-free massive modes

${ m N}=(2,0)$ invariants do not support such vacua

Constructed invariants up to fourth order in derivatives

Abstract

There exists two distinct off-shell ${\mathcal{N}}=2$ supergravities in three dimensions. They are also referred to as ${\mathcal{N}}=(1,1)$ and ${\mathcal{N}}=(2,0)$ supergravities, and they arise from the coupling of the Weyl multiplet to a compensating scalar or vector multiplet, respectively, followed by fixing of conformal symmetries. The ${\mathcal{N}} =(p,q)$ terminology refers to the underlying anti-de Sitter superalgebras $OSp(2,p) \oplus OSp(2,q)$ with $R$-symmetry group $SO(p) \times SO(q)$. We construct off-shell invariants of these theories up to fourth order in derivatives. As an application of these results, we determine the special combinations of the ${\mathcal{N}}=(1,1)$ invariants that admit anti-de Sitter vacuum solution about which there is a ghost-free massive spin-2 multiplet of propagating modes. We also show that the ${\mathcal{N}}=(2,0)$ invariants do not allow such possibility.