Extended double structures and new multiple infinite-dimensional symmetries for the emda theory with two vector fields

The previously proposed extended double (ED)-complex method is used to further study the Einstein-Maxwell-dilaton-axion theory with 2 vector fields (EMDA-2 theory, for brevity). Some ED structures of dimensionally reduced EMDA-2 theory are found. An ED-complex matrix H-potential is constructed and the motion equations are extended to an ED-complex form. Moreover, an ED-duality mapping is introduced and two pairs of ED-complex Hauser-Ernst-type linear systems are established. Basing on these linear systems, new sets of multiple hidden symmetry transformations for the EMDA-2 theory are explicitly constructed. Then these symmetry transformations are verified to constitute multiple infinite-dimensional Lie algebras, each of which is a semidirect product of the Kac-Moody and Virasoro algebras (without centre charges). These results demonstrate that the theory under consideration possesses much richer symmetry structures than previously expected, and the ED-complex method is necessary and more effective.