Intersection numbers on \({\overline{M}}_{g,n}\) and BKP hierarchy.(English)Zbl 1472.83028
Summary: In their recent inspiring paper [“Superintegrability of Kontsevich matrix model”, Eur. Phys. J. C 81, Paper No. 270, 13 p. (2021;doi:10.1140/epjc/s10052-021-09030-x)],A. Mironov andA. Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we provide a similar description for the Brézin-Gross-Witten tau-function. Moreover, we identify both tau-functions of the KdV hierarchy, which describe intersection numbers on the moduli spaces of punctured Riemann surfaces, with the hypergeometric solutions of the BKP hierarchy.
MSC:
| 83C45 | Quantization of the gravitational field |
| 83C80 | Analogues of general relativity in lower dimensions |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 53Z05 | Applications of differential geometry to physics |
Cite
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