The Affine Hidden Symmetry and Integrability of Type IIB Superstring in $AdS_{5} \times S^{5}$

TL;DR

This paper reveals hidden affine symmetries and integrability in the Type IIB superstring on AdS5×S5 by exploiting Hodge duality, Lax connections, and affine algebra structures.

Contribution

It demonstrates how Hodge duality and vierbein transformations expose the affine hidden symmetry and integrability of the superstring in AdS5×S5.

Findings

Identification of affine gl(2,2|4)^{(1)} symmetry

Construction of Lax connections from BPR currents

Derivation of the classical r-matrix

Abstract

In this paper, we motivate how the Hodge dual related with S-duality gives the hidden symmetry in the moduli space of IIB string. Utilizing the static $% \kappa $-symmetric Killing gauge, if we take the Hodge dual of the vierbeins keeping the connection invariant, the duality of Maure-Cartan equations and the equations of motion becomes manifest. Thus by twistly transforming the vierbein, we can express the BPR currents as the Lax connections by a unique spectral parameter. Then we construct the generators of the infinitesimal dressing symmetry, the related symmetric algebra becomes the affine $% gl(2,2|4)^{(1)}$, which can be used to find the classical $r$ matrix.