String theory in AdS sub 3 background

the unitarity of the theory. The role of singleton representation is clarified in the context of logarithmic operators in AdS/CFT correspondence. In this thesis we study string theory in AdS sub 3 background in the context of AdS/CFT correspondence. We discuss unitarity, modular invariance and closure of operator product expansion (OPE) in the theory. A construction of spacetime conformal field theory from worldsheet affine symmetry due to Giveon, Kutasov and Seiberg is presented. The spacetime CFT has the meaning boundary CFT in AdS/CFT correspondence. The knowledge of two dimensional N extended superconformal algebras is used to construct superstrings on AdS sub 3 x N with extended spacetime supersymmetry. A classification of vacua of superstrings on AdS sub 3 is proposed from the knowledge of superconformal algebras in two dimensions. We present some exact solutions of Kniznik-Zamolodochikov (KZ) equation for SL(2, R) WZNW model for four point functions, which have logarithmic singularities of conformally invariant cross ratios, from a simple ansatz. Some asymptotic solutions with logarithmic behaviour are also presented. We analyze the logarithmic solutions and show that they can give rise to logarithmic operators in the theory. It has been shown by OPE analysis and otherwise that representation with SL(2, R) quantum number j = -1/2 play a very special role. The possibility of contribution oj logarithmic operators to the OPE is discussed. We find that OPE can not close or unitary representations if we include the logarithmic operators in the theory. We discuss the implications of logarithmic operators abou