Extended structures and new infinite-dimensional hidden symmetries for the Einstein-Maxwell-dilaton-axion theory with multiple vector fields

A so-called extended elliptical-complex ( EEC) function method is proposed and used to further study the Einstein - Maxwell-dilaton-axion theory with p vector fields (EMDA-p theory, for brevity) for p = 1, 2,.... An Ernst-like 2(k+1) x 2(k+1)( k = [( p + 1)/ 2]) matrix EEC potential is introduced and the motion equations of the stationary axisymmetric EMDA- p theory are written as a so-called Hauser-Ernst-like self-dual relation for the EEC matrix potential. In particular, for the EMDA- 2 theory, two Hauser-Ernst-type EEC linear systems are established and based on their solutions some new parametrized symmetry transformations are explicitly constructed. These hidden symmetries are verified to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac - Moody algebra su( 2, 2) x R( t, t(-1)) and Virasoro algebra ( without centre charges). These results show that the studied EMDA- p theories possess very rich symmetry structures and the EEC function method is necessary and effective.