Infinite-dimensional algebras in dimensionally reduced string theory

Abstract

We examine 4-dimensional string backgrounds compactified over a two torus. There exist two alternative effective Lagrangians containing each two $SL(2)/U(1)$ sigma-models. Two of these sigma-models are the complex and the Kähler structures on the torus. The effective Lagrangians are invariant under two different $O(2,2)$ groups and by the successive applications of these groups the affine $\hat{O}(2,2)$ Kac-Moody is emerged. The latter has also a non-zero central term which generates constant Weyl rescalings of the reduced 2-dimensional background. In addition, there exists a number of discrete symmetries relating the field content of the reduced effective Lagrangians.

13 pages, Latex

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• Target Space Duality in String Theory
• Strong-Weak Coupling Duality in Four Dimensional String Theory
• Strong-Weak Coupling Duality in Three Dimensional String Theory
• Null Killing Vector Dimensional Reduction and Galilean Geometrodynamics
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Cited by in corpus (6)

• Superstring Cosmology
• Inhomogeneous Einstein-Rosen String Cosmology
• Colliding String Waves and Duality
• Duality and Integrability of Two Dimensional String Effective Action
• Mirror Images of String Cosmologies
• Inhomogeneous M-Theory Cosmologies