Superconformal Algebras in Light-cone Gauge Quantization of String Theories on $AdS_3

TL;DR

This paper constructs spacetime superconformal algebras for superstring theories on various $AdS_3$ backgrounds, providing explicit algebraic structures relevant for understanding the boundary theories in the AdS/CFT correspondence.

Contribution

It explicitly constructs N=4, N=3 superconformal algebras on the $AdS_3$ boundary for different superstring backgrounds using light-cone gauge quantization.

Findings

Constructed N=4 large and middle superconformal algebras.

Constructed N=3 superconformal algebra.

Applicable to multiple $AdS_3$ string backgrounds.

Abstract

Motivated by superstring theories on $AdS_3$, we construct spacetime superconformal algebras (SCAs) living on the $AdS_3$ boundary in terms of the transversal physical degrees of freedom. The SCAs constructed are N=4 large, middle algebras, and N=3 algebra, corresponding to superstring theories on $AdS_3 \times S ^3 \times S^3 \times S ^1$, $AdS_3 \times S ^3 \times T ^4 $ and $AdS_3 \times (S^3\times S^3\times S^1)/Z_2$ backgrounds respectively.