New infinite-dimensional multiple-symmetry groups for the Einstein–Maxwell-dilaton–axion theory

The symmetry structures of stationary axisymmetric Einstein–Maxwell-Dilaton–Axion (EMDA) theory are further studied. By using the so-called extended double (ED)-complex function method, the usual Riemann–Hilbert (RH) problem is extended to an ED-complex formulation. Two pairs of ED RH transformations are constructed and they are verified to give infinite-dimensional multiple-symmetry groups of the EMDA theory; each of these symmetry groups has the structure of a semidirect product of a Kac–Moody group Sp(4,R)̂ and a Virasoro group. Moreover, the infinitesimal forms of these RH transformations are calculated and they are found to give exactly the same results as previous work; this demonstrates that the two pairs 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 theoretical studies and new solution generation, etc.