Massive N = 2 supergravity in three dimensions

Abstract: There exists two distinct off-shell (Formula presented.) = 2 supergravities in three dimensions. They are also referred to as (Formula presented.) = (1, 1) and (Formula presented.) = (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 (Formula presented.) = (p, q) terminology refers to the underlying anti-de Sitter superalgebras OSp(2, p) ⊕ OSp(2, q) with R-symmetry group SO(p) × 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 (Formula presented.) = (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 (Formula presented.) =(2,0) invariants do not allow such possibility.