The Critical O(N) Model at Finite Temperature: a comparison of calculations in large N and d = 4 - epsilon

Abstract

In this thesis, we study the properties of conformal field theories (CFTs) at finite temperature. We focus on the CFT defined by the O(N) vector model, which is a scalar field theory that has critical points in 2< d<4. These fixed points of the RG flow define a strongly interacting CFT in d=3. We study observables at these fixed points and at nonzero temperature, including thermal free energy and the correlation functions of local operators. We perform these calculations using a combination of large N and Wilson-Fisher $\epsilon$ expansion techniques.