New Canonical Variables for d=11 Supergravity

Abstract

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 $SO(1,2)\times SO(16)$ invariant reformulation of $d=11$ supergravity given in previous work, 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''.