Alternative Formulation for Duality-Symmetric Eleven-Dimensional   Supergravity Coupled to Super M-5-Brane
  We present an alternative formulation of duality-symmetric eleven-dimensional supergravity with both three-form and six-form gauge fields. Instead of the recently-proposed scalar auxiliary field, we use a simpler lagrangian with a non-propagating auxiliary multiplier tensor field with eight-indices. We also complete the superspace formulation in a duality-symmetric manner. An alternative super M-5-brane action coupled to this eleven-dimensional background is also presented. This formulation bypasses the usual obstruction for an invariant lagrangian for a self-dual three-form field strength, by allowing the self-duality only as a solution for field equations, but not as a necessary condition. 
Hitoshi Nishino