Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models

Abstract

We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully factorized into a product of terms linear in the rank of the matrix and the parameters of the model. We extend our formulas to include both logarthmic and finite-difference deformations, thereby generalizing the celebrated Selberg and Kadell integrals. We conjecture a formula for correlators of two Schur functions in these models, and explain how our results follow from a general orbifold-like procedure that can be applied to any one-matrix model with a single-trace potential.

52 pages, 7 figures

References in corpus (15)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• A Perturbative Window into Non-Perturbative Physics
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Les Houches lectures on matrix models and topological strings
• A direct proof of AGT conjecture at beta = 1
• Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
• Seiberg-Witten prepotential from instanton counting
• Chern-Simons matrix models and Stieltjes-Wigert polynomials
• Think globally, compute locally
• Toda Theory From Six Dimensions
• Matrix models for 2* theories
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• The importance of the Selberg integral
• Phases of planar 5-dimensional supersymmetric Chern-Simons theory
• Rarefied elliptic hypergeometric functions

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