Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 361, Issue 3, Pages 1235-1274Publisher
SPRINGER
DOI: 10.1007/s00220-017-3072-x
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Funding
- DOE [DE-SC0009988]
- Perimeter Institute for Theoretical Physics
- Fundamental Laws Initiative of the Harvard Center for the Fundamental Laws of Nature
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Economic Development and Innovation
- NWO Vici grant
- RFBR [14-02-00627, 15-52-50041-YaF, 16-02-01021, 15-31-20832-mol-a-ved]
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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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