Abstract
There exists two distinct off-shell N $$ \mathcal{N} $$ = 2 supergravities in three dimensions. They are also referred to as N $$ \mathcal{N} $$ = (1, 1) and N $$ \mathcal{N} $$ = (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 N $$ \mathcal{N} $$ = ( 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 N $$ \mathcal{N} $$ = (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 N $$ \mathcal{N} $$ =(2,0) invariants do not allow such possibility.