#### Date of Award

9-2012

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### University

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 *AdS*_{5} x *Y*^{5}, where *Y*^{5} 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 *Y*^{5}.

The second part of this thesis will examine the large-*N* limit of the Kapustin-Willett- Yaakov matrix model. This model computes the *S*^{3} partition function for a CFT dual to M-theory on *AdS*_{4} x* Y*^{7}. 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 *Y*^{7}. A variety of examples are given to support this formula.

#### Recommended Citation

Gulotta, Daniel R. '03, "AdS/CFT in String Theory and M-Theory" (2012). *Doctoral Dissertations*. 19.

https://digitalcommons.imsa.edu/alumni_dissertations/19