|
A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
Gaëtan Borota, Raimar Wulkenhaarb a Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
b Mathematisches Institut, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany
Abstract:
We exhibit the Kontsevich matrix model with arbitrary potential as a BKP tau-function with respect to polynomial deformations of the potential. The result can be equivalently formulated in terms of Cartan–Plücker relations of certain averages of Schur $Q$-function. The extension of a Pfaffian integration identity of de Bruijn to singular kernels is instrumental in the derivation of the result.
Keywords:
BKP hierarchy, matrix models, classical integrability.
Received: January 3, 2024; in final form June 1, 2024; Published online June 11, 2024
Citation:
Gaëtan Borot, Raimar Wulkenhaar, “A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential”, SIGMA, 20 (2024), 050, 16 pp.
Linking options:
https://www.mathnet.ru/eng/sigma2052 https://www.mathnet.ru/eng/sigma/v20/p50
|
Statistics & downloads: |
Abstract page: | 21 | Full-text PDF : | 7 | References: | 10 |
|