General covariance and supersymmetry without supersymmetry.

An unusual four-dimensional generally covariant and supersymmetric SU(2) gauge theory is described. The theory has local degrees of freedom, and is invariant under a local (left-handed) chiral supersymmetry, which is half the supersymmetry of supergravity. The Hamiltonian 3+1 decomposition of the theory reveals the remarkable feature that the local supersymmetry is a consequence of Yang-Mills symmetry, in a manner reminiscent of how general coordinate invariance in Chern-Simons theory is a consequence of Yang-Mills symmetry. It is possible to write down an infinite number of conserved currents, which strongly suggests that the theory is classically integrable. A possible scheme for non-perturbative quantization is outlined. This utilizes ideas that have been developed and applied recently to the problem of quantizing gravity. Pacs numbers: 04.20.Fy, 11.15.-q, 11.30.Pb, 12.60.Jv Typeset using REVTEX