On a new proof of the Okuyama–Sakai conjecture

Abstract

Okuyama and Sakai [JT supergravity and Brézin–Gross–Witten tau-function, J. High Energy Phys. 2020 (2020) 160] gave a conjectural equality for the higher genus generalized Brézin–Gross–Witten (BGW) free energies. In a recent work [D. Yang and Q. Zhang, On the Hodge-BGW correspondence, preprint (2021), arXiv:2112.12736], we established the Hodge-BGW correspondence on the relationship between certain special cubic Hodge integrals and the generalized BGW correlators, and a proof of the Okuyama–Sakai conjecture was also given ibid. In this paper, we give a new proof of the Okuyama–Sakai conjecture by a further application of the Dubrovin–Zhang theory for the KdV hierarchy.