Lie Algebra The Su (m | N) Z <sub> 4 </ Sub> Graded And Green-schwarz Superstring ¦Ê-symmetry Analysis

The superstring theory is one of hotspots in nowadays physics and the major direction of the field theory. After the foundation of the type IIB superstring theory in AdS₅×S⁵ background and the AdS/CFT correspondence,the superstring theory in AdS background have attacked much attention. Theκ-symmetry local supersymmetry of Green-Schwarz superstring action:the action is invariant with respect to the localκ-transformations. It makes the bosonic freedom degree of the system equal to the fermionic freedom degree,so the system can satisfy the requirement of the supersymmetry.This paper have three major works:First, in nowadays literature which study the Green-Schwarz IIB superstring in AdS₅×S⁵ background,there have two descriptions of the action. One is constructed by the Cartan one-form of the current in Lie superalgebra psu(2,2|4).The other is constructed by the Z₄ grading components of the current. By using the representation of the Lie superalgebra psu(2,2|4),we will prove that the two actions are equivalent.Second,there are several superstring in AdS background:the AdS₅×S⁵ super-string, its Lie superalgebra of supercoset space is psu(2,2|4);the AdS₃×S³ super-string,its Lie superalgebra of supercoset space is psu(1, 1|2)²;the AdS₂×S² super-string,its Lie superalgebra of supercoset space is psu(1,1|2).In this paper,we will generate the present AdS superstring to the more ordinary condition—whose Lie superalgebra of supercoset space are su(m|n),and will give the method of Z₄ grading to su(m|n).Third,to the generated AdS superstring,by using a new method,throughout the study of the matrix representation of the Lie superalgebra su(m|n),we analyze theκ-symmetry of the generated models. The conclusion of the analysis can contain the known AdS superstrings,this prove that the new method is correct. And by using the new method,we can get a new AdS superstring which have not been noticed:the AdS₂×S² superstring. The function of theκ-symmetry is to fix the redundant feimiosic freedom degree,in order to make the bosonic freedom degree of the system equal to the fermionic freedom degree. Through the new method,we can get some models which don't have theκ-symmetry,but their bosonic freedom degree are already equal to their fermionic freedom degree. Although we do not know the significance of these models,this is also a beneficial experiment.