Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models

Abstract

We show how the Dijkgraaf-Vafa matrix model proposal can be extended to describe five-dimensional gauge theories compactified on a circle to four dimensions. This involves solving a certain quantum mechanical matrix model. We do this for the lift of the N=1* theory to five dimensions. We show that the resulting expression for the superpotential in the confining vacuum is identical with the elliptic superpotential approach based on Nekrasov's five-dimensional generalization of Seiberg-Witten theory involving the relativistic elliptic Calogero-Moser, or Ruijsenaars-Schneider, integrable system.

11 pages, 2 figures, JHEP3.cls, important references added

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• On Unitary/Hermitian Duality in Matrix Models
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• Nonperturbative Superpotentials and Compactification to Three Dimensions
• Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems
• N=1* in 5 dimensions: Dijkgraaf-Vafa meets Polchinski-Strassler
• New results in $\mathcal{N}=2$ theories from non-perturbative string
• Matrix models for topological strings: exact results in the planar limit
• Superpotentials from flux compactifications of M-theory
• Five-Dimensional Gauge Theories and Unitary Matrix Models
• Vacua of N=1 Supersymmetric QCD from Spin Chains and Matrix Models
• Twisted Six Dimensional Gauge Theories on Tori, Matrix Models, and Integrable Systems