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) X SO(16) invariant reformulation of d = 11 supergravity given by Nicolai [Phys. Lett. 187B (1987) 316], and has some similarities with Ashtekar's reformulation of Einstein's theory. The new bosonic variables fuse the gravitational degrees of freedom with those of the three-index photon A(MNP) in accordance with the hidden symmetries of the dimensionally reduced theory. Although E-8 is not a symmetry of the theory, the bosonic sector exhibits a remarkable E-8 structure, hinting at the existence of a novel type of "exceptional geometry". (C) 1998 Published by Elsevier Science B.V.