Supersymmetric Yang-Mills theory and Riemannian Geometry Original Research Article

We introduce new local gauge invariant variables for N = 1 supersymmetric Yang-Mills theory, explicitly parameterizing the physical Hilbert space of the theory. We show that these gauge invariant variables have a geometrical interpretation, and can be constructed such that the emergent geometry is that of N = 1 supergravity: a Riemannian geometry with vector-spinor generated torsion. Full geometfzation of supersymmetric Yang-Mills theory is carried out, and geometry-independent divergences associated to the inversion of a differential operator with zero modes - that were encountered in the non-supersymmetric case - do not arise in this situation.