AdS/CFT in String Theory and M-Theory

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 &times; Y<super>5</super>, where Y<super>5</super> 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<super>5</super>.

The second part of this thesis will examine the large-N limit of the Kapustin-Willett-Yaakov matrix model. This model computes the S<super>3</super> partition function for a CFT dual to M-theory on AdS4 &times; Y<super>7</super>. 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<super>7</super>. A variety of examples are given to support this formula.