New $$ \mathcal{N} $$ = 2 SuperBMS3 algebra and invariant dual theory for 3D supergravity

Abstract

We have constructed a two dimensional theory dual to 3D asymptotically flat Supergravity in presence of two supercharges with(out) internal R−symmetry. The duals in both the cases are identified with chiral Wess-Zumino-Witten models. Further gauging the theories, we show that the dual of the one without R−symmetry is invariant under the well known N = 2 SuperBMS 3 introduced in Banerjee et.al. 1609.09210 , while for the one with R−symmetry, the dual is invariant under the most generic, so far unknown, quantum N = 2 SuperBMS 3 symmetry. We have also commented on the phase space description of the duals.

Multi-graded Galilean conformal algebras

“…The case of n = 1 2 has been studied in the literature as the N = (2, 0) super-BMS algebra [43]. There has also been interest in N = 1, 2, 4, and (2, 2) super-BMS algebras [40,41,44,45,47].…”

“…Algebras which can be realised using asymmetric Galilean contractions have appeared in the literature before, and include WZW models on non-semisimple Lie groups [36,37,38,39], supersymmetric tensionless strings [9,10], and super-BMS algebras [40,41,42,43,44,45,46,47]. In fact, several of these papers employ inhomogeneous contraction techniques which are special cases of the general construction presented here.…”

On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

“…At the supersymmetric level, the super-BM S 3 algebra appears as the asymptotic symmetry of a three-dimensional minimal supergravity for a suitable set of asymptotically flat boundary conditions [43]. The N -extension of the BM S 3 algebra has subsequently been explored by diverse authors in [44][45][46][47][48]. In particular, the N -extended super-BM S 3 algebras can alternatively be obtained by performing a suitable contraction of the N -extended superconformal algebras [68].…”

“…A minimal supersymmetric extension of the BM S 3 algebra has been shown to describe the asymptotic structure of the N = 1 supergravity in three spacetime dimensions considering suitable boundary conditions [43]. The extensions to N = 2 [44][45][46], N = 4 [47] and N = 8 [48] have later been explored by diverse authors. On the other hand, the supersymmetric extensions of the so-called deformed BM S 3 algebra and the semi-simple enlargement of the BM S 3 algebra remain unknown.…”

Equivalent dual theories for 3D N=2 supergravity

“…One can convince himself that the above action describes a chiral WZW model with gauge group SL(2, R). We refer the readers to [28] for the details computations required to arrive at the above result. The system shows gauge invariance under following (infinitesimal)gauge transformation…”