The Isometries of Low-Energy Heterotic M-Theory
  We study the effective D=4, N=1 supergravity description of five-dimensional heterotic M-theory in the presence of an M5 brane, and derive the Killing vectors and isometry group for the Kahler moduli-space metric. The group is found to be a non-semisimple maximal parabolic subgroup of Sp(4,R), containing a non-trivial SL(2,R) factor. The underlying moduli-space is then naturally realised as the group space Sp(4,R)/U(2), but equipped with a nonhomogeneous metric that is invariant only under that maximal parabolic group. This nonhomogeneous metric space can also be derived via field truncations and identifications performed on Sp(8,R)/U(4) with its standard homogeneous metric. In a companion paper we use these symmetries to derive new cosmological solutions from known ones. 
E. J. Copeland, J. Ellison, A. Lukas, J. Roberts