EXTENDED DOUBLE LINEAR SYSTEMS AND NEW INFINITE-DIMENSIONAL DOUBLE HIDDEN SYMMETRIES FOR STRING EFFECTIVE ACTION

Abstract

Symmetries of the string effective action describing the coupled gravity, dilaton and Kalb–Ramond fields (called EDKR theory for brevity) are studied. A previously proposed extended double-complex method is used and some double structures of the dimensionally reduced (from (2+d)-dim to 2-dim) EDKR theory are found. A 2d × 2d matrix double-complex H-potential is constructed and the field equations are extended to a double-complex formulation. Moreover, a pair of extended double-complex Hauser–Ernst-type linear systems are established, and based on these linear systems, explicit formulations of new hidden double symmetry transformations for the EDKR theory are given. These symmetry transformations constitute double infinite-dimensional Lie algebras, each of which is a semidirect product of the Kac–Moody [Formula: see text] and Virasoro algebras (without center charges). These results demonstrate that the EDKR theory under consideration possesses richer symmetry structures than previously expected.