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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2406.17081 |
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| _version_ | 1866909327491596288 |
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| author | Weller, Quinten |
| author_facet | Weller, Quinten |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Laplace Transform and Quantum Curves Weller, Quinten Mathematical Physics High Energy Physics - Theory Algebraic Geometry 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. |
| title | The Laplace Transform and Quantum Curves |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2406.17081 |