Symplectic Geometry of Supersymmetry and Nonlinear Sigma Model

Abstract

Recently it has been argued, that Poincaré supersymmetric field theories admit an underlying loop space hamiltonian (symplectic) structure. Here shall establish this at the level of a general $N=1$ supermultiplet. In particular, we advocate the use of a superloop space and explain the necessity of using nonconventional auxiliary fields. As an example we consider the nonlinear $σ$-model. Due to the quartic fermionic term, we conclude that the use of superloop space variables is necessary for the action to have a hamiltonian loop space interpretation.