WDVV Equations and Associative Algebras
by
Dmitry Vasiliev
Institute of Theoretical and Experimental Physics, Moscow Institute for Physics and Technology, Russia

Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations appeared in the context of topological string theories [1]. Later they were rediscovered in much large class of physical theories (see [2] and references there in).

There are 2 different geometrical interpretations of WDVV equations. First Boris Dubrovin in [3] developed a description of WDVV solutions with help of Frobenius manifolds. The main drawback of this description is the requirement of constant metric on the moduli space. In many cases this requirement is not satisfied ([2], [4]). Next description is based on the associative algebra of differential forms (which can be build in all known examples of WDVV solutions). In this talk I will discus geometric descriptions of newly developed non-trivial example of solutions to WDVV equations [4] (quasiclassical tau-function of the multi-support solutions to matrix models).

[1] E.Witten, Nucl.Phys. B340 (1990) 281; R.Dijkgraaf, H.Verline and E.Verlinde, Nucl.Phys. B352 (1991) 59.

[2] A. Gorsky, A. Mironov. FIAN-TD-30-00, ITEP-TH-64-00, Nov 2000. 134pp. In Aratyn, H. (ed.) et al.: Integrable hierarchies and modern physical theories* 33-176.

[3] Boris Dubrovin. 204pp. In Montecatini Terme 1993, Integrable systems and quantum groups* 120-348

[4] L. Chekhov, A. Marshakov, A. Mironov, D. Vasiliev. ITEP-TH-04-03, Jan 2003. 15pp. e-Print Archive: hep-th/0301071

Date received: January 31, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cake-45.