Infinite-dimensional algebras in dimensionally reduced string theory

We examine 4-dimensional string backgrounds compactified over a two-torus. There exits two alternative effective Lagrangians containing each two SL(2)U(1) sigma-models. Two of these sigma-models are the complex and 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 Ô(2,2) Lie algebra emerges. 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.