On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions.

Abstract

In this work we obtain known and new supersym_x005F_x0002_metric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semi_x005F_x0002_group expansion method. The super-BMS3, the supercon_x005F_x0002_formal algebra and new infinite-dimensional superalgebras are obtained by expanding the super-Virasoro algebra. The new superalgebras obtained are supersymmetric extensions of the asymptotic algebras of the Maxwell and the so(2, 2)⊕ so(2, 1) gravity theories. We extend our results to the N = 2 and N = 4 cases and find that R-symmetry generators are required. We also show that the new infinite-dimensional structures are related through a flat limit _x005F_x0002_ → ∞. Contents 1 Introduction ..................... 1 2 The semigroup expansion method and Super-Virasoro algebra ........................ 2 3 Known examples ................... 3 3.1 Super-BMS3 algebra .............. 3 3.2 Superconformal algebra ............. 4 3.3 (1, 1) superconformal algebra .......... 6 4 New examples .................... 6 4.1 Supersymmetric extension of the asymptotic algebra of the Maxwell gravity theory ..... 6 4.1.1 Minimal deformed super-BMS _x005F_x0002_ 3 algebra . 7 4.1.2 N = 2 deformed super-BMS _x005F_x0002_ 3 algebra .. 8 4.1.3 N = 4 deformed super-BMS _x005F_x0002_ 3 algebra .. 9 4.2 Supersymmetric extension of the asymptotic algebra of the so (2, 2) ⊕ so (2, 1) gravity theory 10 4.2.1 Minimal enlarged super-BMS3 algebra . 11 a e-mail: rcaroca@ucsc.cl b e-mail: patrick.concha@ucsc.cl c e-mail: ofierro@ucsc.cl d e-mail: evelyn.rodriguez@edu.uai.cl