Massive N $$ \mathcal{N} $$ = 2 supergravity in three dimensions

Abstract

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

Critical $$ \mathcal{N} $$ = (1, 1) general massive supergravity

“…The bosonic part of the most general N = (1, 1) supergravity action that includes up to four derivatives has been derived in [20]. This in particular includes the bosonic part of an N = (1, 1) supergravity version of General Massive Gravity, which will be the focus of this paper and whose bosonic Lagrangian is given by…”

“…In section 2, we review the bosonic Lagrangian and off-shell supersymmetry transformation rules of N = (1, 1) GMG. The fermionic terms of the Lagrangians of N = (1, 1) GMG are not given in [20]. Since our analysis requires the linearized fermionic equations of motion, we will here also construct the full linearized Lagrangian, including fermionic terms, starting from the linearized bosonic Lagrangian and supersymmetry transformation rules.…”

“…We do not consider the N = (2, 0) models in this paper, since unlike N = (1, 1) models these do not seem to have supersymmetric AdS vacua with ghost-free spectrum, when higher-derivative terms are present [20]. We will thus start from the N = (1, 1) theories of [20] and perform a linearization of the theory around its maximally supersymmetric AdS vacuum, to study the spectrum of linearized modes and their linearized supersymmetry transformation rules. This will allow us to identify various critical points where logarithmic modes appear and to study the structure of the supermultiplets to which these logaritmic modes belong.…”

“…The fermionic terms of the N = (1, 1) General Massive Supergravity were not given explicitly in [20]. 1 The complete action for N = (1, 1) General Massive Supergravity was obtained in superspace for the first time using superfield techniques in [23], building on earlier results in [21,22].…”

“…In particular, supersymmetric TMG has been constructed in [16] and N = 1 versions of full GMG have been constructed in [17][18][19]. The bosonic Lagrangian and supersymmetry transformation rules of off-shell N = (2, 0) and N = (1, 1) GMG have been obtained using the method of superconformal tensor calculus in [20], while a full superspace construction is given in [21][22][23]. Some exact supersymmetric solutions of N = (2, 0) and N = (1, 1) GMG have…”