Iib Superstring In The Ads Background Krr Parameterized

A goal is to use a unified theory to describe four basic reciprocitis of the nature, which physicists have pursued over a long period of time.So far,the superstring theory is the most prospective one to achieve this goal.The theory has precise mathematical structure,which makes its spacial symmetry and dimensions quite determinate.That is to say,it is rigid under given major premise.Thus.this theory is a best candidate for a ultimate theory to understand the nature.Therefore it is one of hotspots in nowadays physics.lt can be devided into critical superstrings and noncritical superstrings.Type IIB superstring in AdS₅⊕S⁵ background has the most symmetry in ten dimensional super gravitation,and it is the typical representative of critical superstrings.Thus it has attracted broad attention in physics.Type IIB superstring in AdS₅⊕S⁵ background is one of the noncritical superstrings.There are profound relations between the superstring theory and condensed state physics.They both offer each other in methods,mechanism and principle.They are mutually promotional and influencing.Thereby the development of the superstring theory will bring wide space to the development of condensed state physics from various aspects.The research area of the applicant's master thesis includes a set of identities important in string theory and the parametrisation of IIB superstring models in AdS background.This paper is organized as two parts.In the fist part,the general form of n rank Cγ — γ summation formula is given by using Fierz identity, and under specific conditions Schwarz identity and similar identities are deduced with the summation formula. These identities are needed when studying superstring models.Then the situation of the antisymmetrical charge conjugation matrix C of four dimensions (P = — 1, N = 4) is analyzed.The second part of the paper studies parametrisation of AdS IIB string. Parametrisation plays an important role in superstring theory in AdS space. We must parametrize the models of superstrings when quantizing superstring,solv-ing its equations of motion,etc.KaJlosh et.at gave a method of parametrizing AdSs? S5 superstring (KRR parametrisation method).However,their treatment and derivations are difficult.This paper gives a new method of the KRR parametrisation for two typical superstring models of AdSc,(S)S5 and AdS^QS1.And then their Cartan 1-forms, Maurer-Cartan equations,actions and motion equations are given. Besides AdSs S5 and AdS5 S1 superstring,J4d52 <8> S2, AdSi ? S1 and Polyakov's superstring models can use this new method to parametrize as well.