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arXiv · 1704.05139

Stieltjes-Bethe equations in higher genus and branched coverings with even ramifications

Dmitry Korotkin
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Abstract

We describe projective structures on a Riemann surface corresponding to monodromy groups which have trivial $SL(2)$ monodromies around singularities and trivial $PSL(2)$ monodromies along homologically non-trivial loops on a Riemann surface. We propose a natural higher genus analog of Stieltjes-Bethe equations. Links with branched projective structures and with Hurwitz spaces with ramifications of even order are established. We find a higher genus analog of the genus zero Yang-Yang function (the function generating accessory parameters) and describe its similarity and difference with Bergman tau-function on the Hurwitz spaces.

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Dmitry Korotkin. 2017-04-19. Stieltjes-Bethe equations in higher genus and branched coverings with even ramifications. https://doi.org/10.1016/j.nuclphysb.2017.12.019

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