New Formulation of the Type IIB Superstring Action in $AdS_5 \times S^5$

TL;DR

This paper introduces a new formulation of the type IIB superstring action in $AdS_5 imes S^5$, emphasizing manifest symmetries and simplified Grassmann coordinate dependence, potentially offering advantages over previous models.

Contribution

It develops an alternative superstring formulation using a nonlinear realization of $PSU(2,2|4)$, maintaining manifest bosonic symmetries and providing explicit Grassmann dependence.

Findings

Constructed a superstring action with manifest $PSU(2,2|4)$ symmetry.

Derived simple analytic expressions for Grassmann coordinate dependence.

Established kappa symmetry within the new formulation.

Abstract

Previous studies of the type IIB superstring in an ${AdS_5 \times S^5}$ background are based on a description of the superspace geometry as the quotient space $PSU(2,2|4)/SO(4,1) \times SO(5)$. This paper develops an alternative approach in which the Grassmann coordinates provide a nonlinear realization of $PSU(2,2|4)$ based on the quotient space $PSU(2,2|4)/SU(2,2) \times SU(4)$, and the bosonic coordinates are described as a submanifold of $SU(2,2) \times SU(4)$. This formulation keeps all bosonic symmetries manifest, and it provides the complete dependence on the Grassmann coordinates in terms of simple analytic expressions. It is used to construct the superstring world-sheet action in a form in which the $PSU(2,2|4)$ symmetry is manifest and kappa symmetry can be established. This formulation might have some advantages compared to previous ones, but this remains to be demonstrated.