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

TL;DR

This paper explores the algebraic and geometric structures of the SL(2, R) WZW model on an AdS3 background, analyzing operator product expansions and differential equations to deepen understanding of string theory in curved spacetime.

Contribution

It introduces a comprehensive algebraic and geometric analysis of the SL(2, R) WZW model, including new differential equations and methods for modifying algebraic operators.

Findings

Consistency of OPE relations on a hypersurface in CP3

Derivation of three nonlinear first-order differential equations

Application of generalized functions and integral geometry to algebraic operators

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.