Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity

TL;DR

This paper explores the relationship between threebrane configurations near Calabi-Yau singularities and their dual string theories on AdS spaces, focusing on the conifold case and its associated supersymmetric gauge theory.

Contribution

It establishes a detailed correspondence between threebrane theories at Calabi-Yau singularities and specific ${ m N}=1$ supersymmetric gauge theories, extending the AdS/CFT framework.

Findings

String theory on $AdS_5\times X_5$ corresponds to a specific ${\cal N}=1$ gauge theory.

The paper provides a detailed description of the gauge theory for the conifold singularity.

It generalizes the AdS/CFT correspondence to singular Calabi-Yau geometries.

Abstract

Just as parallel threebranes on a smooth manifold are related to string theory on $AdS_5\times {\bf S}^5$, parallel threebranes near a conical singularity are related to string theory on $AdS_5\times X_5$, for a suitable $X_5$. For the example of the conifold singularity, for which $X_5=(SU(2)\times SU(2))/U(1)$, we argue that string theory on $AdS_5\times X_5$ can be described by a certain ${\cal N}=1$ supersymmetric gauge theory which we describe in detail.