Green-schwarz String Of Conserved Currents Reconciliation And Transformation As Well As Related Issues

String theory is among the frontier areas of contemporary physics,which in many aspects shade light to condensed matter physics including research methods and results.There are several important stages in the development of string ,one of which is the Green-Schwarz(GS) superstring.Maldacena's conjecture about ADS/CFT correspondence greatly stimulates the study of GS string in AdS space. Metsaev and Tseytlin gave the model in AdS₅×S⁵ space which has been extensively studying with great interest.In 2003,Bena,Polchinski and Roiban found the flat connections with a free parameter of this model.Thus there are many infinitely conserved quantities in the system. After this finding,the study of the flat connections and integrability of the model and other similar models became a hot topic again in string theory. One of the important issues of integrable system is the solution transformation, which produces a set of new solutions from an existing one.This is the main topic of the thesis,which contains the following new results.1.By Polyakov's action in string theory we study the minimum surface and expand the Weierstrass formula to N dimensional space.2.Prove that the flat connections of the GS string in AdS₅×S⁵ space satisfy the equations of motion and Virasoro Constraint and correspond to a set of new solutions, which gives the construction of new solutions from an existing one.3.The above construction is proved to be valid for the GS string in AdS₃×S³ space.4.Give theκ- symmetry in target space for GS string in AdS₃×S³ space.