Two-dilaton theories in two dimensions from dimensional reduction

Dimensional reduction of generalized gravity theories or string theories ge nerically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D = 4 theories and cosmology, many models contain more than just one scalar field (e.g., inflation, Higgs, quintessence). Our pre sent work is restricted to two-dimensional gravity theories with only two d ilatons which nevertheless allow a large class of physical applications. Th e notions of factorizability, simplicity and conformal simplicity. Einstein form, and Jordan form are the basis of an adequate classification. We show that practically all physically motivated models belong either to the clas s of factorizable simple theories (e.g., dimensionally reduced gravity. bos onic. string) or to factorizable conformally simple theories (e.g., spheric ally reduced scalar-tensor theories). For these theories a first order form ulation is constructed straightforwardly. As a consequence an absolute cons ervation law can be established. (C) 2001 Academic Press.