Constructing Gauge Theory Geometries from Matrix Models

Abstract

We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or anti-symmetric matter, broken by a tree level superpotential to a product subgroup involving U(N_i) and SO(N_i) or Sp(N_i/2) factors. The relevant geometry is encoded by a non-hyperelliptic Riemann surface, which we extract from the exact loop equations. We also show that O(1/N) corrections can be extracted from a logarithmic deformation of this surface. The loop equations contain explicitly subleading terms of order 1/N, which encode information of string theory on an orientifolded local quiver geometry.

arXiv comment52 pages

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Cited by in corpus (21)

• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories
• (Anti)symmetric matter and superpotentials from IIB orientifolds
• On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models
• Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies
• Cubic curves from matrix models and generalized Konishi anomalies
• Higher order loop equations for A_r and D_r quiver matrix models
• Chiral field theories from conifolds
• Chern-Simons Matrix Models and Unoriented Strings
• Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models
• Chiral field theories, Konishi anomalies and matrix models
• On Sp(0) factors and orientifolds
• Irregular conformal block, spectral curve and flow equations
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Improved matrix-model calculation of the N=2 prepotential
• Quivers via anomaly chains
• Remarks on the analytic structure of supersymmetric effective actions
• Chiral rings, anomalies and loop equations in N=1* gauge theories
• Konishi Anomalies and Curves without Adjoints
• Effective superpotential for U(N) with antisymmetric matter
• Quantum Geometries of $A_2$