Supersymmetry and loop space geometry

Abstract

We present a conceptually new interpretation of Poincaré supersymmetric theories in terms of loop space symplectic geometry. We argue, that the fermionic part of a supersymmetric action can be viewed as a (pre) symplectic two form in the loop space of bosonic fields, and the bosonic part of the action can be constructed by contracting the pertinent loop space symplectic potential with a model independent vector field. Our approach entails a novel auxiliary field formalism. It also opens a new point of view to a large class of problems, including the mechanism of supersymmetry breaking, structure of topological field theories and even aspects of quantum integrability.