On higher Brézin-Gross-Witten tau-functions

Abstract

In this paper, we consider the higher Brézin--Gross--Witten tau-functions, given by the matrix integrals. For these tau-functions we construct the canonical Kac--Schwarz operators, quantum spectral curves, and $W^{(3)}$-constraints. For the simplest representative we construct the cut-and-join operators, which describe the algebraic version of the topological recursion. We also investigate a one-parametric generalization of the higher Brézin--Gross--Witten tau-functions.

arXiv comment34 pages, published version

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• Relations on ${\overline{\mathcal{M}}}_{g,n}$ and the negative $r$-spin Witten conjecture
• KP integrability through the $x-y$ swap relation
• Degenerate and irregular topological recursion