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arXiv · 1108.0885

Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations

A. Mironov·A. Morozov·S. Natanzon
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Abstract

Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra (CAA). As a corollary, partition functions of topological theory always satisfy the generalized WDVV equations. We consider the Hurwitz partition functions, associated in this way with the CAA of cut-and-join operators. The ordinary Hurwitz numbers for a given number of sheets in the covering provide trivial (sums of exponentials) solutions to the WDVV equations, with finite number of time-variables. The generalized Hurwitz numbers from arXiv:0904.4227 provide a non-trivial solution with infinite number of times. The simplest solution of this type is associated with a subring, generated by the dilatation operators tr X(d/dX).

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A. Mironov, A. Morozov, S. Natanzon. 2011-08-03. Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations. https://doi.org/10.1007/jhep11(2011)097

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