$τ$-function for analytic curves

Details $τ$-function for analytic curves $τ$-function for analytic curves

2000-05-26

arxiv.org/abs/hep-th/0005259v1

Random matrices and their applications, MSRI publications,vol.40, 285,2001, Cambridge University Press

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, no figures, prepared for Proccedings of MSRI Workshop ``Matrix Models and Painlev\'e Equations'', Berkeley (USA) 199

Scientific paper

We review the concept of $\tau$-function for simple analytic curves. The $\tau$-function gives a formal solution to the 2D inverse potential problem and appears as the $\tau$-function of the integrable hierarchy which describes conformal maps of simply-connected domains bounded by analytic curves to the unit disk. The $\tau$-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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