$\tau$-function for analytic curves
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2000
- DOI:
- 10.48550/arXiv.hep-th/0005259
- arXiv:
- arXiv:hep-th/0005259
- Bibcode:
- 2000hep.th....5259K
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 13 pages, no figures, prepared for Proccedings of MSRI Workshop ``Matrix Models and Painlev\'e Equations'', Berkeley (USA) 1999