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Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity

Igor R. Klebanov, Edward H. Witten

Open publisher page 913 citations

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.

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What this paper is about

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.

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Available 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.

Key concepts: Conifold, Singularity, Calabi–Yau manifold, Singularity theory, String theory, String (physics), F-theory, Gauge theory

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