Non relativistic field theories and Black holes

Abstract

This thesis is dedicated to studying field theories and has three parts. The first two parts are on aspects of non relativistic field theories. By taking 2 classical field theories namely, Landau's theory of superfluidity and Yang Mills theories, whose relativistic versions are well known, we study features of non relativistic versions of these theories. Importantly, we use 2 different ways to approach the problem studying the non relativistic field theory of a known relativistic field theory. In case of fluids, we follow the procedure of [1] by studying fluids in one higher dimension in a space time carrying a null killing vector. The non relativistic physics is arrived at by doing a null reduction along this direction. In case of Yang Mills theories, we arrive a the non relativistic equations of motion by sending the speed of light c to infinity in consistent ways. We find that we can do this in more than one way. The third part of this thesis is on stodying certain aspects of black holes in string theory, particularly on the construction of supergravity solutions which could be microstates of certain black holes. We do this by reviewing the works of [2] and [3] and study some topics in string theory.