SYMPLECTIC-GEOMETRY OF SUPERSYMMETRY AND NONLINEAR SIGMA-MODEL

Recently it has been argued, that Poincare 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 introduced by A.Yu. Morozov, A.J. Niemi and K. Palo, Nucl. Phys. B 377 (1992) 295, and the necessity of using nonconventional auxiliary fields. As an example we consider the nonlinear sigma-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.