Minimal Green-schwarz Superstring Krr Parameterization

The theory of superstrings,as the theory of low dimension field, methods in the theory of field are widely used in many domain of condensed matter physics and they have a very important significance in the study of condensed matter physics;at the same time,some important mechanism of the theory of condensed matter physics are closed related to some the theory of fields,such as soliton,scattering amplitude and so on.So with the thoroughly researching on the theory of superstrings,it must can provide some useful help to condensed matter physics from aspects of backgrounds and methods .The AdS/CFT correspondence has played an important role and has a widely use in string/M-theory.It is important to study the AdS/CFT correspondence in the cases with lower dimension space,since as a Toy mosel,they are easier to handle for better understanding the corresponsence.In this paper,we focus on the parametrisation of the AdS₂ (?) S¹ string,then generalize our results to other AdS string.The research area of the applicant's master thesis includes the parametrisation of IIB superstring models in AdS₂ (?) S¹ background.The paper is organized as two parts.The action and equations of motion of super-strings propagating in some AdS background is formulated by current generally. Whereas the current should satisfy Maurer-Cartan equations implied by the structure of the su-peralgebra.These Cartan 1-forms are not independent variables.We must parametrize the supergroup because the action should be expressed by independent mechanical variables when quantizing superstring and solving its equations of motion.In the first part,it is to study su(1,1|1) Lie superalgebra's coset model of IIB superstrings on AdS₂ (?) S¹ background.we get the commutation relations of sit(1,1|1) Lie superal-gebra and Maurer—Cartan equation by the the indicial matrix.The second part of the paper studies parametrisation of IIB superstring models in AdS₂ (?) S¹ back-ground.Kallosh et.at gave a method of parametrizing AdS₅ (?)S⁵ string(KRR parametrisation method).However,their treatment and derivations are difficult.This paper gives three new methods of the KRR parametrisation for the simplest superstring model of AdS₂ (?) S¹ (classical KRR parametrisation,Chiral gauge by fixng theκsymmetry parametrisation,Light cone gauge by fixng theκsymmetry parametrisation).And then their Cartan 1-forms,Maurer—Cartan equations are given.