Title:

String theory and conformal field theory

In this thesis we consider some aspects of two dimensional Conformal Field Theory and their connection to String Theory. We have also studied some aspects of supersymmetry of MTheory on Ricciflat seven manifolds with 4form fluxes. We concentrate mainly on certain supersymmetric extensions of the coset models due to Goddard, Kent and Olive (GKO). These models are known as the KazamaSuzuki (KS) models and they are characterized by their N = 2 superconformal symmetry. Two series of the KS models enjoy a duality called levelrank duality which can be described roughly as duality between the dimension of the target space and the level of coset. We believe that the pathintegral approach is the closest in spirit to string theory. Therefore, we formulate the levelrank duality of KS models in the pathintegral approach by using the realization of GKO cosets as gauged WessZuminoNovikovWitten (gaugedWZNW) models. We derive, for a class of KS models, an expression for the partition function which is symmetric in the parameters of the levelrank duality. We compute the central charge of the models from this expression which matches that of Kazama and Suzuki in the operator approach. We then work out the target space metric and the dilation of the gaugedWZNW model based on the GKO coset SU(3)/(SU(2) x U(1)). It turns out to be quite a complicated metric with a nontrivial dilation. We verify, as a consistency check, that they satisfy the appropriate string theory effective equations of motion. We then argue that this background can arise naturally in type II string theory compactified down to AdS_{3} space. We then turn to Eleven Dimensional Supergravity which is the low energy limit of Mtheory. We adopt a metric ansatz which is a warped product of four dimensional Minkowski space and a (noncompact) seven manifold with 4form fluxes turned on it. We derive the condition for unbroken supersymmetry with fluxes and nontrivial warpfactor. We show that the same condition implies that the seven manifold is conformal to a Ricciflat manifold. We also point out the limitation of some naive ansatze about the structure of the Killing spinor. At this stage we are unable to give an explicit solution to the supersymmetry condition.
