Some Algebro-Geometric Aspects of The SL(2, R) Wess-Zumino-Witten Model of Strings on an ADS$_{3}$ Background

Abstract

The SL(2, R) WZW model of strings on an ADS3 background is investigated in the spirit of J.Maldacena's and H.Ooguri's approach (hep-th/0001053) and (hep-th/0005183). Choosing a standard, but most general three-variable parametrization of the SL(2, R) group element g, the system of equations for the Operator Product Expansion (OPE) relations is analysed. In the investigated SL(2, R) case, this system is consistent if each three points on the complex plane lie on a certain hypersurface in CP3. A system of three nonlinear first-order differential equations has been obtained for the parametrization functions. It was demonstrated also how the mathematical apparatus of generalized functions and integral geometry can be implemented in order to modify the integral operators, entering the Kac-Moody and Virasoro algebras.

LATEX (Sci.Word, amsmath style), 8 pages, no figures; to appear in the Proceedings of the First Advanced Research Workshop "Gravity, Astrophysics and Strings at the Black Sea", June 10-16, 2002, Bulgaria; also an abridged version of the talk at the International Workshop "Quantum Gravity and Superstrings",July 11-18, 2002, Dubna, Russia