Generalized Conifolds and 4d N=1 SCFT

TL;DR

This paper explores the connection between string theory on generalized conifold singularities and four-dimensional N=1 superconformal field theories, analyzing RG flows and geometric duals.

Contribution

It extends the study of AdS/CFT correspondence to generalized conifold singularities with ADE classification, detailing the geometry and IR fixed points of N=1 SCFTs.

Findings

Identification of IR fixed points from ADE deformations

Construction of near-horizon supergravity solutions

Analysis of RG flows connecting supersymmetric fixed points

Abstract

This paper lays groundwork for the detailed study of the non-trivial renormalization group flow connecting supersymmetric fixed points in four dimensions using string theory on AdS spaces. Specifically, we consider D3-branes placed at singularities of Calabi-Yau threefolds which generalize the conifold singularity and have an ADE classification. The $\mathcal{N}=1$ superconformal theories dictating their low-energy dynamics are infrared fixed points arising from deforming the corresponding ADE $\mathcal{N}=2$ superconformal field theories by mass terms for adjoint chiral fields. We probe the geometry with a single $D3$-brane and discuss the near-horizon supergravity solution for a large number $N$ of coincident $D3$-branes.