arXiv subjects

Paolo Gregori

Publications and source records attributed to Paolo Gregori.

5 recordsLinked to original sources

arXiv2026

Volumes of moduli spaces of bordered Klein surfaces

We investigate volumes of moduli spaces of bordered Klein surfaces, which include non-orientable surfaces. On these moduli spaces, the top form introduced by Norbury diverges as the lengths of 1-sided geodesics approach zero. However, when integrated over Gendulphe's regularised moduli space, on which the systole of 1-sided geodesics is bounded below by $ε\in\mathbb{R}_{>0}$, it returns a finite value. We derive an explicit formula for the volume of the moduli space of two-bordered real projective planes and of one-bordered Klein bottles --- the latter utilises Norbury's extension of the Mirzakhani--McShane identities to non-orientable surfaces. We then relate these results to refined topological recursion, showing that, for a fixed refinement parameter, the volumes of moduli spaces of Klein surfaces with Euler characteristic $-1$ are governed by this procedure. For general topologies, both approaches remain incomplete due to several difficulties, which we discuss in this work. Together with our results, this initiates the search for a geometric recursive structure governing the volumes of moduli spaces of bordered Klein surfaces, whose natural formulation may lie within a suitably extended version of refined topological recursion.

math.GT↗

arXiv2023

Resurgent Asymptotics of Jackiw-Teitelboim Gravity and the Nonperturbative Topological Recursion

Jackiw-Teitelboim dilaton-quantum-gravity localizes on a double-scaled random-matrix model, whose perturbative free energy is an asymptotic series. Understanding the resurgent properties of this asymptotic series, including its completion into a full transseries, requires understanding the nonperturbative instanton sectors of the matrix model for Jackiw-Teitelboim gravity. The present work addresses this question by setting-up instanton calculus associated to eigenvalue tunneling (or ZZ-brane contributions), directly in the matrix model. In order to systematize such calculations, a nonperturbative extension of the topological recursion formalism is required -- which is herein both constructed and applied to the present problem. Large-order tests of the perturbative genus expansion validate the resurgent nature of Jackiw-Teitelboim gravity, both for its free energy and for its (multi-resolvent) correlation functions. Both ZZ and FZZT nonperturbative effects are required by resurgence, and they further display resonance upon the Borel plane. Finally, the resurgence properties of the multi-resolvent correlation functions yield new and improved resurgence formulae for the large-genus growth of Weil-Petersson volumes.

hep-th↗

arXiv2023

From Minimal Strings towards Jackiw-Teitelboim Gravity: On their Resurgence, Resonance, and Black Holes

Two remarkable facts about JT two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensemble is described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e., changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series). These analyses are first done via spectral geometry, at both perturbative and nonperturbative levels, addressing the resurgent large-order growth of perturbation theory, alongside a calculation of nonperturbative instanton-actions and corresponding Stokes data. This calculation requires an algorithm to reach large-order, which is valid for arbitrary two-dimensional topological gravity. String equations -- as derived from the GD construction of the resolvent -- are analyzed in both multicritical and minimal string theoretic contexts, and studied both perturbatively and nonperturbatively (always matching against the earlier spectral-geometry computations). The resulting solutions, as described by resurgent transseries, are shown to be resonant. The large matter-central-charge limit is addressed -- in the string-equation context -- and, in particular, the string equation for JT gravity is obtained to next derivative-orders, beyond the known genus-zero case (its possible exact-form is also discussed). Finally, a discussion of gravitational perturbations to Schwarzschild-like black hole solutions in these minimal-string models, regarded as deformations of JT gravity, is included - alongside a brief discussion of quasinormal modes.

hep-th↗

arXiv2023

Resurgent large genus asymptotics of intersection numbers

In this paper, we present a novel approach for computing the large genus asymptotics of intersection numbers. Our strategy is based on a resurgent analysis of the $n$-point functions of such intersection numbers, which are computed via determinantal formulae, and relies on the presence of a quantum curve. With this approach, we are able to extend the recent results of Aggarwal for Witten-Kontsevich intersection numbers with the computation of all subleading corrections, proving a conjecture of Guo-Yang, and to obtain new results on $r$-spin and Theta-class intersection numbers.

math.AG↗

arXiv2017

More on the New Large $D$ Limit of Matrix Models

In this paper, we extend the recent analysis of the new large $D$ limit of matrix models to the cases where the action contains arbitrary multi-trace interaction terms as well as to arbitrary correlation functions. We discuss both the cases of complex and Hermitian matrices, with $\text{U}(N)^{2}\times\text{O}(D)$ and $\text{U}(N)\times\text{O}(D)$ symmetries respectively. In the latter case, the new large $D$ limit is consistent for planar diagrams; at higher genera, it crucially requires the tracelessness condition. For similar reasons, the large $N$ limit of tensor models with reduced symmetries is typically inconsistent already at leading order without the tracelessness condition. We also further discuss some interesting properties of purely bosonic models pointed out recently and explain that the standard argument predicting a non-trivial IR behaviour in fermionic models à la SYK does not work for bosonic models. Finally, we explain that the new large $D$ scaling is consistent with linearly realized supersymmetry.

hep-th↗