From topological recursion to wave functions and PDEs quantizing hyperelliptic curves
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866913181210771456 |
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| author | Eynard, Bertrand Garcia-Failde, Elba |
| author_facet | Eynard, Bertrand Garcia-Failde, Elba |
| contents | Starting from loop equations, we prove that the wave functions constructed from topological recursion on families of degree $2$ spectral curves with a global involution satisfy a system of partial differential equations, whose equations can be seen as quantizations of the original spectral curves. The families of spectral curves can be parametrized with the so-called times, defined as periods on second type cycles, and with the poles. These equations can be used to prove that the WKB solution of many isomonodromic systems coincides with the topological recursion wave function, which proves that the topological recursion wave function is annihilated by a quantum curve. This recovers many known quantum curves for genus zero spectral curves and generalizes this construction to hyperelliptic curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_07795 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | From topological recursion to wave functions and PDEs quantizing hyperelliptic curves Eynard, Bertrand Garcia-Failde, Elba Mathematical Physics Analysis of PDEs Exactly Solvable and Integrable Systems 34M56, 34M55, 34M60, 34E20, 35J10, 60B20 Starting from loop equations, we prove that the wave functions constructed from topological recursion on families of degree $2$ spectral curves with a global involution satisfy a system of partial differential equations, whose equations can be seen as quantizations of the original spectral curves. The families of spectral curves can be parametrized with the so-called times, defined as periods on second type cycles, and with the poles. These equations can be used to prove that the WKB solution of many isomonodromic systems coincides with the topological recursion wave function, which proves that the topological recursion wave function is annihilated by a quantum curve. This recovers many known quantum curves for genus zero spectral curves and generalizes this construction to hyperelliptic curves. |
| title | From topological recursion to wave functions and PDEs quantizing hyperelliptic curves |
| topic | Mathematical Physics Analysis of PDEs Exactly Solvable and Integrable Systems 34M56, 34M55, 34M60, 34E20, 35J10, 60B20 |
| url | https://arxiv.org/abs/1911.07795 |