Date of Award

9-2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Princeton University

Department

Physics

First Advisor

Christopher P. Herzog, Ph.D.

Keywords

string theory, M-theory, AdS/CFT correspondence, quiver gauge theories

Subject Categories

Elementary Particles and Fields and String Theory | Physical Sciences and Mathematics | Physics

Abstract

The AdS/CFT correspondence is a powerful tool that can help shed light on the relationship between geometry and field theory.

The first part of this thesis will focus on the construction of theories dual to Type IIB string theory on AdS5 x Y5, where Y5 is a toric Sasaki-Einstein manifold. This thesis will introduce a consistency condition called "proper ordering" and demonstrate that it is equivalent to several other previously known consistency conditions. It will then give an efficient algorithm that produces a consistent field theory for any toric Sasaki-Einstein Y5.

The second part of this thesis will examine the large-N limit of the Kapustin-Willett- Yaakov matrix model. This model computes the S3 partition function for a CFT dual to M-theory on AdS4 x Y7. One of the main results will be a formula that relates the distribution of eigenvalues in the matrix model to the distribution of holomorphic operators on the cone over Y7. A variety of examples are given to support this formula.

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