Aspects of finite temperature field theories in Ads/CFT

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Brigante, Mauro

Advisor dc:contributor.advisor

• Hong Liu.

• Physics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/45454

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/45454