On field theory from gravity duals

Hockings, James Rufus (2002) On field theory from gravity duals. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

We review strings and branes in general, and then introduce the AdS/CFT Correspondence. The original work begins with an examination of the geometry for N = 4 on moduli space. We find a neat prescription for the encoding of the gravity solution in terms of the dual gauge theory. We next try to extend this to the N = 2* scenario, but encounter problems due to the gravity solution giving unexpected renormalization. Then we consider the correspondence applied to two field theories off their moduli space. We encounter unexpected problems with N = 2* again, but are successful in interpreting the Leigh-Strassler case. Finally, we apply the AdS/CFT correspondence to examine N = 4 super Yang-Mills at finite U(1)_R charge density, using the spectrogravity backgrounds around spinning D3 branes. We complete the interpretation of the field theory duals of these backgrounds by interpreting the non-supersymmetric naked singularity class of the solutions. We find that these naked spinning D-brane distributions describe the coulomb branch at finite density. At a critical density a phase transition occurs to a spinning black brane representing the deconfined phase where the higgs vevs have evaporated. We also extend our analysis to include finite temperature. We perform a free energy calculation to determine the phase diagram of the coulomb branch at finite density and temperature.