The Laplace Transform and Quantum Curves
| Autor: | Weller, Quinten |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A Laplace transform that maps the topological recursion (TR) wavefunction to its $x$-$y$ swap dual is defined. This transform is then applied to the construction of quantum curves. General results are obtained, including a formula for the quantisation of many spectral curves of the form $e^xP_2(e^y) - P_1(e^y) = 0$ where $P_1$ and $P_2$ are coprime polynomials; an important class that contains interesting spectral curves related to mirror symmetry and knot theory that have, heretofore, evaded the general TR-based methods previously used to derive quantum curves. Quantum curves known in the literature are reproduced, and new quantum curves are derived. In particular, the quantum curve for the $T$-equivariant Gromov-Witten theory of $\mathbb{P}(a,b)$ is obtained. Comment: 20 pages (17 plus references). Second version cleaned up minor typos, added details to the proof of the main theorem, and corrected a statement that the relation between the Gromov-Witten invariants for the complex weighted projective line and topological recursion was unknown. The quantum curve associated with these Gromov-Witten invariants was then derived |
| Databáze: | arXiv |
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