|
This article is cited in 4 scientific papers (total in 4 papers)
WKB expansion for a Yang–Yang generating function and the Bergman tau function
M. Bertolaab, D. A. Korotkina a Concordia University, Department of Mathematics and Statistics, Montréal, Québec, Canada
b International School for Advanced
Studies (SISSA), Area of Mathematics, Trieste, Italy
Abstract:
We study symplectic properties of the monodromy map of second-order equations on a Riemann surface whose potential is meromorphic with double poles. We show that the Poisson bracket defined in terms of periods of the meromorphic quadratic differential implies the Goldman Poisson structure on the monodromy manifold. We apply these results to a WKB analysis of this equation and show that the leading term in the WKB expansion of the generating function of the monodromy symplectomorphism (the Yang–Yang function introduced by Nekrasov, Rosly, and Shatashvili) is determined by the Bergman tau function on the moduli space of meromorphic quadratic differentials.
Keywords:
Riemann surface, monodromy map, symplectic map generating function, tau function, Goldman bracket.
Received: 17.10.2019 Revised: 02.12.2020
Citation:
M. Bertola, D. A. Korotkin, “WKB expansion for a Yang–Yang generating function and the Bergman tau function”, TMF, 206:3 (2021), 295–338; Theoret. and Math. Phys., 206:3 (2021), 258–295
Linking options:
https://www.mathnet.ru/eng/tmf9834https://doi.org/10.4213/tmf9834 https://www.mathnet.ru/eng/tmf/v206/i3/p295
|
Statistics & downloads: |
Abstract page: | 231 | Full-text PDF : | 47 | References: | 17 | First page: | 6 |
|