Rigid supersymmetric backgrounds of 3-dimensional Newton-Cartan supergravity

Abstract

Recently, a non-relativistic off-shell formulation of three dimensional NewtonCartan supergravity was proposed as the c → ∞ limit of three dimensional N = 2 supergravity [1]. In the present paper we study supersymmetric backgrounds within this theory. Using integrability constraints for the non-relativistic Killing spinor equations, we explicitly construct all maximally supersymmetric solutions, which admit four supercharges. In addition to these solutions, there are 1 2 -BPS solutions with reduced supersymmetry. We give explicit examples of such backgrounds and derive necessary conditions for backgrounds preserving two supercharges. Finally, we address how supersymmetric backgrounds of N = 2 supergravity are connected to the solutions found here in the c → ∞ limit.

Minimal N = 4 $$ \mathcal{N}=4 $$ topologically massive supergravity

“…The bosonic body of such a superspace is warped AdS 3 spacetime associated with the Killing vector c a (x) = C a (z)| θ=0 . Warped AdS 3 spacetimes have been discussed in detail in the literature, see [39][40][41][42][43] and references therein. In the N = 2 supersymmetric case, the (super)space geometry of maximally supersymmetric warped (2,0) AdS backgrounds was described in [11] and further elaborated in [34].…”

“…14 However, maximally supersymmetric warped AdS backgrounds do exist in extended supergravity, N > 1, if the structure group includes not only the Lorentz group SL(2, R) but also a nontrivial R-symmetry group. For instance, the structure group for N = (2, 0) AdS supergravity is SL(2, R) × U(1) R , and thus this theory possesses maximally supersymmetric warped AdS backgrounds, which were described in [11,34] using the superspace techniques, and some time later in [41,42] using the component approach. On the other hand, the structure group for N = (1, 1) 12 Not all values of α lead to distinct supergroups, since the supergroups defined by the parameters α ±1 , −(1 + α) ±1 and −α ±1 (1 + α) ∓1 are isomorphic [36,37].…”

A New Look at Newton–Cartan Gravity

“…Following 21,22 one can then apply localization techniques to extract exact results out of such theories. The first step in this program for the case of NC gravity has already been taken in 23 .…”

Disformal transformation in Newton–Cartan geometry

“…For example, the boundary geometry in Lifshitz holography is described by torsional NCG [7,9]. For related studies on supergravity in NCG with or without torsion, see [44][45][46][47][48]. All in all, whether there is torsion or not can lead to very different results.…”