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On a new proof of the Okuyama-Sakai conjecture

Reviews in Mathematical Physics, ISSN: 1793-6659, Vol: 35, Issue: 9
2023
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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.

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