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arXiv · hep-th/0005259

$τ$-function for analytic curves

I. K. Kostov·I. Krichever·M. Mineev-Weinstein·P. Wiegmann·A. Zabrodin
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Abstract

We review the concept of $τ$-function for simple analytic curves. The $τ$-function gives a formal solution to the 2D inverse potential problem and appears as the $τ$-function of the integrable hierarchy which describes conformal maps of simply-connected domains bounded by analytic curves to the unit disk. The $τ$-function also emerges in the context of topological gravity and enjoys an interpretation as a large $N$ limit of the normal matrix model.

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I. K. Kostov, I. Krichever, M. Mineev-Weinstein, P. Wiegmann, A. Zabrodin. 2000-05-26. $τ$-function for analytic curves. https://arxiv.org/abs/hep-th/0005259

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