GPRS asymptotic formulas for super Weil–Petersson volumes

Prove the GPRS conjectural large-genus asymptotic formulas for super Weil–Petersson volumes with prescribed boundary lengths and for super intersection numbers, including the exact universal normalization constant in the leading asymptotics, for boundary lengths satisfying the stated growth conditions.

Background

Section 1.3 introduces the conjectural asymptotics proposed by Griguolo, Papalini, Russo, and Seminara for super Weil–Petersson volumes with prescribed boundary components whose lengths satisfy L_i = o(√g), together with the corresponding asymptotics for super intersection numbers. The paper denotes these statements as the GPRS conjecture.

Theorem 1.7 establishes the same asymptotic forms only up to a universal multiplicative constant C, while the conjecture specifies the exact normalization. Thus the exact version of the conjecture is not completely resolved by the results stated in the paper.

References

The conjectural formulae (cf. [8, (2.13) and (2.11a)]) of large genus asymptotics of super Weil-Petersson volumes with given boundary components satisfying Li « g was recently proposed by Griguolo-Papalini-Russo-Seminara [8] by applying resurgence theory to analyze the matrix model of JT supergravity, which we will refer to as the GPRS conjecture. We reformulated it following the notation (1.1) as below.

Conjecture 1.1 (GPRS [8]).

— Large genus asymptotics of super Weil-Petersson volumes  (2501.07848 - Huang, 14 Jan 2025) in Conjecture 1.1, Section 1.3