Extended Superconformal Algebras on AdS_{3}

TL;DR

This paper explores supersymmetric extensions of the Virasoro algebra on AdS_{3} boundary, identifying specific affine Lie superalgebras that realize extended superconformal symmetries.

Contribution

It demonstrates how free field realizations of affine Lie superalgebras correspond to boundary superconformal algebras with N=1, 2, and 4 supersymmetries.

Findings

osp(1|2)^{(1)} yields N=1 superconformal algebra

sl(1|2)^{(1)} yields N=2 superconformal algebra

sl(2|2)^{(1)} yields N=4 superconformal algebra

Abstract

We study a supersymmetric extension of the Virasoro algebra on the boundary of the anti-de Sitter space-time AdS_{3}. Using the free field realization of the currents, we show that the world-sheet affine Lie superalgebras osp(1|2)^{(1)}, sl(1|2)^{(1)} and sl(2|2)^{(1)} provide the boundary N=1,2 and 4 extended superconformal algebras, respectively.