Double structures and double symmetries for the Einstein-Kalb-Ramond theory

We further study the two-dimensional reduced Einstein-Kalb-Ramond (EKR) theory in the axisymmetric case by using the so-called double-complex function method. We find a doubleness symmetry of this theory and exploit it so that some double-complex d x d matrix Ernst-like potential can be constructed, and the associated equations of motion can be extended into a double-complex matrix Ernst-like form. Then we give a double symmetry group O(d, d; R(J)) for the EKR theory and verify that its action can be realized concisely by a double-complex matrix, form generalization of the fractional linear transformation on the Ernst potential. These results demonstrate that the theory under consideration possesses more and richer symmetry structures. Moreover, as an application, we obtain an infinite chain of double-sol ut ions of the EKR theory showing that the double-complex method is more effective. Some of the results in this paper cannot be obtained by the usual (nondouble) scheme.