Double Structures and Multiple Symmetry Groups for the Reduced 4-Dimensional String Background Equations

Abstract

By using the extended double complex method proposed previously, the 1-loop string background equations with axion and dilaton fields in 4 dimensions with two commuting Killing symmetries and δc = 0 are reduced essentially to two double Ernst σ-models. Then the string Geroch group acting on the solution space is extended to a multi-fold version of a semidirect product of the string Geroch group and the Virasoro group. The usual string Geroch group is just one component of a subgroup in the multi-fold semidirect product group. It is also found that a dobule Z2 symmetry exists for every case of the 4-dimensional reduced string equations and for most of the cases here, this Z2 symmetry is new and cannot be obtained in the usual (non-double) scheme. These results show that the reduced string background equations considered possess more and richer symmetry structures than previously expected. Moreover, a double form of string soliton method is briefly described and, as an application, a multiple family of soliton solutions of the considered reduced string equations is given, which shows that the double method is more effective.