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arXiv · 2306.01501

A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential

Gaëtan Borot·Raimar Wulkenhaar
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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-Pl\"ucker 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.

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Gaëtan Borot, Raimar Wulkenhaar. 2023-06-02. A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential. https://doi.org/10.3842/sigma.2024.050

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