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arXiv · 1611.03142

Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models

Clay Cordova·Ben Heidenreich·Alexandr Popolitov·Shamil Shakirov
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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.

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Clay Cordova, Ben Heidenreich, Alexandr Popolitov, Shamil Shakirov. 2016-11-10. Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models. https://doi.org/10.1007/s00220-017-3072-x

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