$Z_2$ Symmetry of $AdS_3 \times S^3 \times S^3 \times S^1$ Superstrings

TL;DR

This paper explores the role of $Z_2$ symmetry in the large $N=4$ superconformal algebra to develop a more complete free field realization, impacting the search for dual conformal field theories of superstrings in a specific $AdS_3$ background.

Contribution

It introduces a new perspective on the $Z_2$ symmetry to achieve a more comprehensive free field realization of the algebra, enhancing understanding of the dual CFTs.

Findings

Identifies the significance of $Z_2$ symmetry in the superconformal algebra.

Proposes a more complete free field realization beyond existing models.

Implications for the dual CFTs of superstrings in $AdS_3$ backgrounds.

Abstract

We discuss the importance of $Z_2$ symmetry of large $N=4$ superconformal algebra for finding its free field realization that is more complete than the most commonly used one, that is, the Sevrin, Troost and van Proeyen realization. This in turn has implications for the search of a conformal field theory dual to superstrings moving in $AdS_3 \times S^3 \times S^3 \times S^1$ background.