Light-cone Specification Under The Green-schwarz Superstring Hamiltonian And The Advection Of The Symmetric Invariance

The AdS/CFT correspondence between the N=4 SYM theory and the type IIB superstring theory in AdS5×S5 space implies various relations between their respective properties. One property that attracted much attention recently is integrability. The study of the integrability and solution transformation of the string non-linear sigma-model is important for the better understanding of the The AdS/CFT correspondence.This thesis consists of two parts. In Chapter 2, We parameterize the Green-Schwarz IIB superstring in AdS5×S5 background in the light-cone gauge by the method of Metsaev and Tseytlin in AdS5 and by the method of Kallosh, Rahmfeld, Rajaraman and H. Lu in S5. Then we obtain the explicit form of the corresponding Maurer-Cartan 1-forms and Green-Schwarz action in the fermionic light-coneκ-symmetry gauge. Then we consider fixing the bosonic light-cone gauge by choosing x+=τand y9=σ, and we derive a gauge-fixed Lagrangian which is linear in general velocities after eliminating the world sheet metric. We also give the light-cone Hamiltonian and Poisson bracket of the model. Since this system is free, the hierarchy of infinite conserved quantities induce solution transformations due to Jacobi identity.In Chapter 3, We show that for Green-Schwarz superstring in AdS3×S3, the one-parameter family of flat currents retains zero-curvature condition and keeps the variation relations under K-symmetry, diffeomorphism, local Lorentz SO(1,2)×SO(3) and global SU(1,1│2)2 symmetry transformations respectively, which indicates that the flat currents exist in allκ-symmetry gauge fixed cases. As a result, we find that the infinite conserved quantities are invariant under these transformations and independent of the gauge choice of the system.