BKP-relations in Kontsevich model with arbitrary potential

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Abstract

The Kontsevich matrix model with M 3-potential is known to provide a KdV τ -function. There are generalisations to r-KdV, with time variables expressed in terms of eigenvalues of an external matrix. We report on joint work with G. Borot in which we exhibit the Kontsevich matrix model with arbitrary potential as a BKP τ -function with respect to further polynomial deformations of the potential. This gives rise to an infinite hierarchy of quadratic relations between moments of the Kontsevich measure generalised to any potential. Our result needs an extension of de Bruijn’s Pfaffian integration identity to singular kernels. In work in progress with K. Harengel we try to understand whether in case of M 4-potential, where the 1{N -leading moments are known explicitly, the BKP relations are just combinatorial identities or amount to infinitely many non-linear differential equations for the planar 2-point function.

Speakers from the University of Münster

Wulkenhaar, Raimar

Professur für Reine Mathematik (Prof. Wulkenhaar)