Topics in gauge/gravity correspondence.

String theory suggests a mathematical equivalence between certain gauge theories and theories of gravity known as AdS/CFT correspondence. We will discuss it and its generalization in the context of cones over Sasaki-Einstein spaces. The type IIB supergravity solution with metric as a direct product of five dimensional Anti de Sitter space and five dimensional Sasaki-Einstein space is dual to superconformal gauge theories with product gauge groups known as quiver gauge theories. Chiral symmetry breaking is an important property of QCD---the theory of strong interactions. We will show that a small complex supersymmetric deformation of the solution breaks chiral symmetry on the field theory side. We will also consider another deformation of the solution by blowing up 4-cycles. On the gauge theory side, it corresponds to giving a vacuum expectation value to a non-mesonic operator. Some quiver gauge theories possess a discrete symmetry under the action of a Heisenberg group which seems to be broken by Seiberg duality. We will show that the symmetry is manifest in the space of Seiberg dual phases. A way to systematically classify and find new supergravity solution is the G-structure technique. We will apply it to classify supergravity solutions in the case of N = 4, D = 5 ungauged supergravity.Ph.D.Pure SciencesTheoretical physicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126771/2/3276240.pd