Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers
arXiv:2304.07433 · doi:10.1016/j.geomphys.2024.105306
Abstract
Given a spectral curve with exponential singularities (which we call a "transalgebraic spectral curve"), we extend the definition of topological recursion to include contributions from the exponential singularities in a way that is compatible with limits of sequences of spectral curves. This allows us to prove the topological recursion/quantum curve correspondence for a large class of transalgebraic spectral curves. As an application, we find that Atlantes Hurwitz numbers, which were previously thought to fall outside the scope of topological recursion, satisfy (our extended version of) topological recursion, and we construct the corresponding quantum curve directly from topological recursion.
arXiv comment57 pages, final preprint version. Published in J. Geom. Phys
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