Non-perturbative data for Weil-Petersson volumes and intersection numbers using ordinary differential equations

A bstract 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 $$ \mathcal{N} $$ N =1 JT supergravity, proving a conjecture of Stanford and Witten. Our predictions yield new growth formulae for the cases of $$ \mathcal{N} $$ N =2 and $$ \mathcal{N} $$ N =4 JT supergravity.