Iib Superstring In The Ads <sub> 5 </ Sub> (?) S ~ 5 Background Hidden Symmetry

AdS5 S5 space is the one of the maximally supersymmetric solution of the type IIB supergravity. According to AdS/CFT duality conjecture, type IIB superstring theory on AdS5 S5 background corresponds to D = 4, N = 4 Super Yang-Mills theory which has the superconformal symmetry: SU(2,2|4). The AdS/CFT correspondence set up the relation between the superstring theory which is a theory of gravity to supersymmetric gauge theory with no gravity at all.There are two approaches to describe superstring theory: Green-Schwarz formulation and Ramond-Neveu-Schwarz formulation. The introduction of local supersymmetry on worldsheet results in the Ramond-Neveu-Schwarz model, and global supersymmetry in the ten-dimensional spacetime directly yields the Green-Schwarz superstring. The Green-Schwarz superstring theory is a covariant theory. The manifestly super-symmetric Green-Schwarz approach seems more adequate one when the IIB superstring on AdS5 S5 background with Ramond-Ramond 5-form field strength.The Green-Schwarz IIB superstring on AdS5 S5 background can be considered as a non-linear a model where the fields take values in the coset superspace The superstring action has global SU (2,2|4) super-invariance and local k symmetry. There is mutually dual between the Euler-Lagrange equation of motion and the Maurer-Cartan equation. We introduce a twisted dual transformation which is defined by difference rotation of bosonic fields and fermionic fields respectively. The bosonic fields rotate oppositely along the direction ofthe lightcone of the worldsheet. The fermionic fields rotate oppositely according to k symmetry. The symmetry of the twisted dual is the symmetry of the moduli space. This hidden symmetry generate infinitely many nonlocal currents on the worldsheet.There exists a dual symmetry between the equations of motion and the Maurer- Cartan equations of the type IIB superstring on AdS5 S5. We generalize the finite dual transformation to the infinitesimal dual transformation by the twisted dual. We also obtain the Lax connexion and the compatibility condition for this integrable system. In terms of the twisted dual parameter, we obtain the affine superalgebra su(2,2|4). We have a relation between the integrable system of IIB superstring on AdS5 S5 and affined Toda theory. We can get the r matrix by the Lax connexion and make quantized procedure of type IIB superstring on AdS5 S5 background.