Massive 3D supergravity

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.

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

“…The equations for H µν and h agree precisely with those arising in the N = (1, 0) GMG model [4,6] whose spectrum was studied in detail in [7], extending earlier results of [21] for the bosonic model. For "non-critical" values of the couplings summarized by the condition m −2 Ω(η + − η − )(|η + | − 1)(|η − | − 1) = 0, these equations describe the UIRs of SO(2, 2) with lowest weight (E 0 , s), and where ℓ −1 E 0 is the lowest energy, and s is the helicity, their values given by…”

“…Given the Lagrangian (3.11) with parameter choices (3.13), the only parity violating contribution comes from the Lorentz Chern-Simons term and it is given by ± Note that this result precisely matches with the three dimensional N = (1, 0) model [6] since vacuum expectation values for the R-symmetry gauge field V µ and the imaginary part of the auxiliary scalar S vanish (3.15).…”

“…Ghosts are absent for m 2 > 0 and σ ≤ 0 [5,6,26]. Next, we note that the linearized fluctuation of the field D vanishes.…”

“…A particular combinations of these invariants constitute the supersymmetric generalization of the so-called "New Massive Gravity" which has the virtue of being ghost-free [5]. Some of their properties, such as their supersymmetric vacua and spectrum about AdS 3 vacuum, have also been studied [4,6,7].…”

“…Here, we do not attempt to calculate the central charge as in the original argument of Brown-Henneaux [29], but consider the bosonic truncation of the N = (1, 1) generalized massive gravity (3.14) as in [4,6]. For parity-preserving theories with higher derivative extensions, the left and right central charges are given by [30,31] …”