Action with Manifest Duality for Maximally Supersymmetric   Six-dimensional Supergravity
  We perform explicitly the toroidal compactification of eleven dimensional supergravity to six dimensions and present its action in a manifestly $SO(5,5)\over SO(5)\times SO(5)$ invariant form using the recently proposed covariant formulation of theories involving chiral fields. 
GianCarlo De Pol, Harvendra Singh, Mario Tonin