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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.03351 |
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| _version_ | 1866908842059628544 |
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| author | Johnson, Clifford V. Rodrigues, João |
| author_facet | Johnson, Clifford V. Rodrigues, João |
| contents | Recently, a new method was introduced for computing $V_{g,1}(b)$, the Weil-Petersson volumes of the moduli space of Riemann surfaces of genus $g$ with one geodesic boundary of length $b$, various supersymmetric generalizations of them, as well as analogous quantities in intersection theory. The physical setting is the computation of a certain one-point function in a variety of models of 2D gravity for which there is a double-scaled random matrix model (RMM) description. The method combines perturbative solutions of two ordinary differential equations (ODEs), the Gel'fand-Dikii resolvent equation, and the RMM's string equation. In this paper, we extend the method to extract non-perturbative information about the $V_{g,1}(b)$ (and their analogues) that is naturally contained in the full ODEs, providing an efficient prescription for computing the transseries coefficients of the one-point correlation function, fully incorporating ZZ-brane and FZZT-brane effects, and for the first time, mixed ZZ-FZZT-effects. We use as a case study the (2,3) minimal string, computing perturbative and non-perturbative quantities, comparing them to perturbative results from topological recursion, and to results from the recent non-perturbative topological recursion framework. As a particularly powerful further application we provide general predictions for the large order in $g$ growth of $V_{g,1}(b)$, and apply them to JT gravity, finding agreement with known results, and for analogous quantities in ${N} {=} 1$ JT supergravity, proving a conjecture of Stanford and Witten. Our predictions yield new growth formulae for the cases of ${N} {=} 2$ and ${N}{=}4$ JT supergravity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_03351 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-perturbative data for Weil-Petersson volumes and intersection numbers using ordinary differential equations Johnson, Clifford V. Rodrigues, João High Energy Physics - Theory Mathematical Physics Recently, a new method was introduced for computing $V_{g,1}(b)$, the Weil-Petersson volumes of the moduli space of Riemann surfaces of genus $g$ with one geodesic boundary of length $b$, various supersymmetric generalizations of them, as well as analogous quantities in intersection theory. The physical setting is the computation of a certain one-point function in a variety of models of 2D gravity for which there is a double-scaled random matrix model (RMM) description. The method combines perturbative solutions of two ordinary differential equations (ODEs), the Gel'fand-Dikii resolvent equation, and the RMM's string equation. In this paper, we extend the method to extract non-perturbative information about the $V_{g,1}(b)$ (and their analogues) that is naturally contained in the full ODEs, providing an efficient prescription for computing the transseries coefficients of the one-point correlation function, fully incorporating ZZ-brane and FZZT-brane effects, and for the first time, mixed ZZ-FZZT-effects. We use as a case study the (2,3) minimal string, computing perturbative and non-perturbative quantities, comparing them to perturbative results from topological recursion, and to results from the recent non-perturbative topological recursion framework. As a particularly powerful further application we provide general predictions for the large order in $g$ growth of $V_{g,1}(b)$, and apply them to JT gravity, finding agreement with known results, and for analogous quantities in ${N} {=} 1$ JT supergravity, proving a conjecture of Stanford and Witten. Our predictions yield new growth formulae for the cases of ${N} {=} 2$ and ${N}{=}4$ JT supergravity. |
| title | Non-perturbative data for Weil-Petersson volumes and intersection numbers using ordinary differential equations |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2601.03351 |