The Hodge Dual Symmetry of the Green-Schwarz Superstring in $Ad{S}_5\otimes S^5$

The hidden symmetry and an infinite set non-local conserved currents of the Green-Schwarz superstring on $Ad{S}_5\otimes S^5$ 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${}^{\text{cite}bpr}$ as the Lax connections by a unique spectral parameter.