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Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models

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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 logarithmic 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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Authors and Affiliations

  1. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Clay Córdova

  2. Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada

    Ben Heidenreich

  3. Institute for Theoretical and Experimental Physics, Moscow, Russia, 117218

    Alexandr Popolitov

  4. Institute for Information Transmission Problems, Moscow, Russia, 127994

    Alexandr Popolitov & Shamil Shakirov

  5. Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE, Amsterdam, The Netherlands

    Alexandr Popolitov

  6. Society of Fellows, Harvard University, Cambridge, MA, 20138, USA

    Shamil Shakirov

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  1. Clay Córdova
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  2. Ben Heidenreich
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  3. Alexandr Popolitov
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Correspondence to Clay Córdova.

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Córdova, C., Heidenreich, B., Popolitov, A. et al. Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models. Commun. Math. Phys. 361, 1235–1274 (2018). https://doi.org/10.1007/s00220-017-3072-x

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