New canonical variables for d=11 supergravity

A set of new canonical variables for d=11 supergravity is proposed which renders the supersymmetry variations and the supersymmetry constraint polynomial. The construction is based on the SO(1,2)×SO(16) invariant reformulation of d=11 supergravity given by Nicolai [Phys. Lett. 187B (1987) 316], and has some similarities with Ashtekarʹs reformulation of Einsteinʹs theory. The new bosonic variables fuse the gravitational degrees of freedom with those of the three-index photon AMNP in accordance with the hidden symmetries of the dimensionally reduced theory. Although E8 is not a symmetry of the theory, the bosonic sector exhibits a remarkable E8 structure, hinting at the existence of a novel type of “exceptional geometry”.