New boundary conditions for (extended) AdS ₃ supergravity

Abstract

In this work, we build the most general boundary conditions for N = (1, 1) and N = (2, 2) extended supergravity. We show that for the loosest set of boundary conditions, their asymptotic symmetry algebras are two copies of the osp (1 | 2) k and osp (2 | 2) k algebra, respectively. Then, we restrict the gauge fields on the boundary conditions in order to obtain supersymmetric extensions of the Brown-Henneaux and Troessaert boundary conditions. Furthermore, for N = 1 and N = 2 (extended) supergravity we show the supersymmetric extensions of Avery-Poojary-Suryanarayana boundary conditions.

Exploring new boundary conditions for $$\mathcal {N}=(1,1)$$ extended higher-spin $$AdS_3$$ supergravity

“…This method recently has also been applied to flat-space [28] and chiral higher-spin gravity [29] which showed a new class of boundary conditions for higher-spin theories in Ad S 3 . The simplest extension of the Grumiller and Riegler's analysis for the most general N = (1, 1) and N = (2, 2) extended higher spin supergravity theory in Ad S 3 is the Valcárcel's paper [30] where the asymptotic symmetry algebra for the loosest set of boundary conditions for (extended) supergravity has been obtained. This is an alternative to the non-chiral Drinfeld-Sokolov type boundary conditions.…”

“…After repeating the same algebra for¯ -sector, one can say that the asymptotic symmetry algebra for the most general boundary conditions of N = (1, 1) supergravity is two copies of the affine osp(1|2) k algebra as in Ref. [30].…”

N-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions

“…It is well assumed that a three-dimensional (super)gravity theory can be described by a Chern-Simons (CS) action as a gauge theory offering us an interesting toy model to approach higherdimensional theories [1][2][3][4][5][6][7][8][9][10][11]. There has been a growing interest to go beyond Poincaré and AdS (super)groups to describe (super)gravity theories in order to study new models with different physical content [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In a previous work [27], we presented a new class of three-dimensional supergravity theories based on the Maxwell and AdS-Lorentz superalgebras.…”

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

“…Although the model contains an explicit three dimensional part, its variation is two dimensional. Thus W ZW model describes the dynamics of two dimensional fields g. Such reductions have been mostly performed for asymptotically AdS 3D gravity [9][10][11][12][13][14][15][16][17]. Reduction of ISO(2, 1) Chern-Simons to WZW model was first studied in [18].…”