NEW INFINITE-DIMENSIONAL DOUBLE SYMMETRY GROUPS FOR THE EINSTEIN–KALB–RAMOND THEORY

Abstract

The symmetry structures of the dimensionally reduced Einstein–Kalb–Ramond (EKR) theory is further studied. By using a so-called extended double (ED)-complex method, the usual Riemann–Hilbert (RH) problem is extended to an ED-complex formulation. A pair of ED RH transformations are constructed and they are verified to give infinite-dimensional double symmetry groups of the EKR theory, each of these symmetry groups has the structure of semidirect product of Kac–Moody group [Formula: see text] and Virasoro group. Moreover, the infinitesimal forms of these RH transformations are calculated out and they are found to give exactly the same results as previous, these demonstrate that the pair of ED RH transformations in this paper provide exponentiations of all the infinitesimal symmetries in our previous paper. The finite forms of symmetry transformations given in the present paper are more important and useful for theoretic studies and new solution generation, etc.