Year: 2024
Type: article
Abstract: For a given spectral curve, the theory of topological recursion generates two different families \omega_{g,n} ω g , n and \omega_{g,n}^\vee ω g , n ∨ of multi-differentials, which are for algebraic spectral curves related via the universal x-y x − y duality formula. We propose a formalism to extend the validity of the x-y x − y duality formula of topological recursion from algebraic curves to spectral curves with exponential variables of the form e^x=F(e^y) e x = F ( e y ) or e^x=F(y)e^{a y} e x = F ( y ) e a y with F F rational and a a some complex number, which was in principle already observed in [Commun. Number Theory Phys. 13, 763 (2019); J. Lond. Math. Soc. 109, e12946 (2024)]. From topological recursion perspective the family \omega_{g,n}^\vee ω g , n ∨ would be trivial for these curves. However, we propose changing the n=1 n = 1 sector of \omega_{g,n}^\vee ω g , n ∨ via a version of the Faddeev’s quantum dilogarithm which will lead to the correct two families \omega_{g,n} ω g , n and \omega_{g,n}^\vee
Source: SciPost Physics
Author: Alexander Hock
Institution: University of Oxford
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4401813486