Skip to Main content Skip to Navigation

# Quantization of hyper-elliptic curves from isomonodromic systems and topological recursion

Abstract : We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of spectral Darboux coordinates on the moduli space of meromorphic $sl2$-connections on $P1$ and argue that the topological recursion produces a 2g-parameter family of associated tau functions, where 2g is the dimension of the moduli space considered. We apply this procedure to the 6 Painlevé equations which correspond to $g=1$ and consider a $g=2$ example.
Keywords :
Document type :
Journal articles
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-02423721
Contributor : Inspire Hep Connect in order to contact the contributor
Submitted on : Tuesday, October 19, 2021 - 2:12:14 PM
Last modification on : Thursday, November 18, 2021 - 2:48:23 PM

### File

article-vf3.pdf
Files produced by the author(s)

### Citation

Olivier Marchal, Nicolas Orantin. Quantization of hyper-elliptic curves from isomonodromic systems and topological recursion. J.Geom.Phys., 2022, 171, pp.104407. ⟨10.1016/j.geomphys.2021.104407⟩. ⟨hal-02423721⟩

### Metrics

Les métriques sont temporairement indisponibles