Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity

TL;DR

The paper generalizes the AdS/CFT correspondence to D3-branes at Calabi–Yau conical singularities, focusing on the conifold and the AdS5 × T^{1,1} background. It provides a concrete N=1 SU(N) × SU(N) gauge theory with bi-fundamental matter and a specific superpotential that flows to a conformal fixed point, whose moduli and operator spectrum match the geometry of the conifold and its T^{1,1} base. The work establishes precise symmetry and marginal deformation analyses, linking field theory data to supergravity modes and offering a blueprint for holographic duals on less-symmetric Einstein spaces. It also discusses extending these ideas to M-theory, connecting AdS7 × X4 and AdS4 × X7 backgrounds to branes at conical singularities and illustrating a broader holographic framework beyond the original AdS5 × S5 paradigm.

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.