On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

TL;DR

This paper explores supersymmetric extensions of asymptotic symmetries in three-dimensional spacetime, introducing new superalgebras via semigroup expansion, including extensions related to Maxwell and gravity theories, with extensions to higher supersymmetry cases.

Contribution

It presents novel supersymmetric extensions of asymptotic symmetry algebras in three dimensions using the semigroup expansion method, including new superalgebras related to Maxwell and gravity theories.

Findings

Derived super-$BMS_3$ and superconformal algebras.

Constructed new superalgebras extending Maxwell and gravity symmetries.

Connected structures through a flat limit $\, ightarrow\, ext{infinity}$.

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 $\ell \rightarrow \infty$.