New infinite-dimensional hidden symmetries for the Einstein-Maxwell-dilaton-axion theory

An Ernst-like 4 x 4 matrix complex potential is introduced and the motion equations of the stationary axisymmetric Einstein-Maxwell-dilaton-axion (EMDA) theory are written as a so-called Hauser-Ernst (HE)-like self-dual relation for the matrix potential. Two HE-type linear systems are established and based on which some explicit formulations of new parametrized symmetry transformations for the EMDA theory are constructed. These hidden symmetries are proved to constitute an infinite-dimensional Lie algebra, which is a semidirect product of the Kac-Moody algebra sp(4, R) · R(t,t-1) and Virasoro algebra (without centre charges). As a part of that, the positive-half sub-Kac-Moody algebra sp(4, R) · R(t) corresponds to the Geroch-like symmetries for the EMDA theory