Double structures and double symmetries for the Einstein-Maxwell-dilaton-axion theory

By using the so-called double-complex function method, it is found that the stationary axisymmetric D = 4 Einstein-Maxwell-Dilaton-Axion system can be written in a double-complex matrix Ernst-like form. Then the double symmetry symplectic group Sp((4, R(J)) of the theory and its double-complex fractional linear realization are given. These results demonstrate that the theory considered possesses more and richer symmetry structures than previously expected. Moreover, as an application, an infinite chain of double-solutions of the problem is obtained, which shows that the double-complex method is more effective. Some of the results of this paper cannot be obtained by the usual (non-double) scheme.