INFINITE-DIMENSIONAL ALGEBRAS IN DIMENSIONALLY REDUCED STRING THEORY

We examine 4-dimensional string backgrounds compactified over a two-to rus. There exist two alternative effective Lagrangians containing each two SL(2)IU(I) sigma-models. Two of these sigma-models are the comple x and Kahler structures on the torus. The effective Lagrangians are in variant under two different O(2, 2) groups and by the successive appli cations of these groups the affine (O) over cap(2,2) Lie algebra emerg es. The latter has also a non-zero central term which generates consta nt Weyl rescalings of the reduced 2-dimensional background. In additio n, there exists a number of discrete symmetries relating the field con tent of the reduced effective Lagrangians.