Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.Includes bibliographical references (p. 119-124).In this dissertation I study some properties of field theories at finite temperature using the AdS/CFT correspondence. I present a general proof of an "inheritance principle" satisfied by a weakly coupled SU(N) (or U(N)) gauge theory with adjoint matter on a class of compact manifolds (like S3). In the large N limit, finite temperature correlation functions of gauge invariant single-trace operators in the low temperature phase are related to those at zero temperature by summing over images of each operator in the Euclidean time direction. As a consequence, various non-renormalization theorems of Af = 4 Super Yang-Mills theory on S3 survive at finite temperature. I use the factorization of the worldsheet to isolate the Hagedorn divergences at all orders in the genus expansion and to show that the Hagedorn divergences can be re-summed by introducing double scaling limits. This allows one to extract the effective potential for the thermal scalar. For a string theory in an asymptotic anti-de Sitter (AdS) space time, the same behavior should arise from the boundary YangMills theory. Introducing "vortex" contributions for the boundary theory at finite temperature I will show that this is indeed the case and that Yang-Mills Feynman diagrams with vortices can be identified with contributions from boundaries of moduli space on the string theory side. Finally, I consider the shear viscosity to entropy density ratio in conformal field theories dual to Einstein gravity with curvature square corrections. For generic curvature square corrections I show that the conjectured viscosity bound can be violated. I present the calculation in three different methods in order to check consistency. Gauss-Bonnet gravity is also considered, for any value of the coupling. It is shown that a lower bound (lower than the KSS bound) on the shear viscosity to entropy density ratio is determined by causality in the boundary theory.by Mauro Brigante.Ph.D
