On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

Abstract

In this work we obtain known and new supersymmetric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semigroup expansion method. The super-BM S 3 , the superconformal 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 ℓ → ∞. Conclusions 316 Acknowledgment 32

Three-dimensional exotic Newtonian supergravity theory with cosmological constant

“…Moreover, the S-expansion method provides us with the non-vanishing components of the invariant tensor of the S-expanded (super)algebra in terms of the invariant tensor of the original (super)algebra. It is important to mention that both expansion mechanisms have been useful not only to construct new relativistic (super)gravity theories [60][61][62][63][64][65][66][67][68][69][70][71][72][73] but also at the non-relativistic level [43,47,50,51,[74][75][76][77][78][79][80].…”

“…Such subspace decomposition satisfies (3.9). On the other hand, let S (1) L = {λ 0 , λ 1 , λ 2 } be the relevant semi-group whose elements satisfy the following multiplication law [73]:…”

Non-relativistic three-dimensional supergravity theories and semigroup expansion method

“…The semigroup choice is not arbitrary and comes from the expansion relation presented at the level of the asymptotic symmetry. Indeed, as it was shown in [82], the conformal superalgebra can be obtained by expanding the super Virasoro one using S (1) L as the relevant semigroup, while generalizations of the superconformal symmetry are found using S M . It is interesting to notice that the same semigroup used to relate diverse infinite-dimensional superalgebras can be considered at the NR level.…”

“…Within the S-expansion procedure the expanded (super)algebra is obtained by combining the structure constants of a Lie (super)algebra with the multiplication law of a semigroup S. In addition, the S-expansion method provides us with the non-vanishing components of the invariant tensor for the expanded (super)algebra, which are crucial to construct CS actions. The S-expansion mechanism not only has been useful at the NR level 2 [22,27,[65][66][67][68] but also to obtain novel relativistic symmetries [69][70][71][72][73], superalgebras [74][75][76][77][78][79], and asymptotic symmetries [80][81][82], among others.…”

Three-dimensional exotic Newtonian gravity with cosmological constant

“…Such subspace decomposition satisfies (3.9). On the other hand, let S (1) L = {λ 0 , λ 1 , λ 2 } be the relevant semigroup whose elements satisfy the following multiplication law [72]:…”