The Hodge Dual Symmetry of the Green-Schwarz Superstring in $AdS_5 \otimes S^5$

TL;DR

This paper reveals a hidden symmetry in the Green-Schwarz superstring on $AdS_5 imes S^5$, connecting the Hodge duality of equations to non-local conserved currents and expressing them via Lax connections with a spectral parameter.

Contribution

It demonstrates that the Hodge duality between Maurer-Cartan and equations of motion uncovers a hidden symmetry, enabling the expression of conserved currents as Lax connections with a spectral parameter.

Findings

Identification of hidden symmetry via Hodge duality.

Expression of conserved currents as Lax connections.

Connection between Maurer-Cartan equations and equations of motion.

Abstract

The hidden symmetry and an infinite set non-local conserved currents of the Green-Schwarz superstring on $AdS_5\otimes S^5$ have been pointed out by Bena et al. In this paper, we shown that the Hodge dual between the Maurer-Cartan equation and the equation of motion gives the hidden symmetry in the moduli space of Green-Schwarz superstring. Thus by twisty transforming the vielbeins, we can express the currents of the paper$^{\cite{bpr}}$ as the Lax connections by a unique spectral parameter.