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-BMS_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 mathfrak {so}(2,2)oplus mathfrak {so}(2,1) gravity theories. We extend our results to the mathcal {N}=2 and mathcal {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 ell rightarrow infty .
Highlights
A semi-simple enlargement of the B M S3 algebra has been introduced in [34] corresponding to the asymptotic symmetry of a gravity theory invariant under the so-called AdS-Lorentz algebra which can be seen as a semi-simple enlargement of the Poincaré algebra
For completeness we provide with the N = 4 enlarged superB M S3 algebra which corresponds to the infinite-dimensional lift of the N = 4 AdS-Lorentz superalgebra endowed with internal symmetry algebra
By expanding the super-Virasoro algebra we have found the minimal supersymmetric extensions of the asymptotic algebras of the Maxwell gravity [17] and so (2, 2) ⊕ so (2, 1) gravity [34] theories defined in three spacetime dimensions
Summary
We apply the S-expansion to the super-Virasoro algebra in order to introduce novel supersymmetric extensions of known asymptotic symmetries. The new infinite-dimensional superalgebras obtained correspond to the supersymmetric extensions of the deformed B M S3 algebra and the enlarged B M S3 algebra. They can be seen as the infinite-dimensional lifts of the Maxwell and AdS-Lorentz superalgebra introduced in [52] and [53], respectively. 4, we present novel supersymmetric extensions of the deformed and enlarged B M S3 algebras applying different semigroups to the super-Virasoro algebra.
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