The Heterotic Supersymmetric Sigma Model in the Canonical Exterior Formalism

Abstract

Starting from a classical 2D superconformal theory described by the Wess–Zumino–Witten action, the canonical exterior formalism on group manifold for the heterotic supersymmetric sigma model is constructed. The motion equations of the dynamical field and the constraints are found and analyzed from the geometric point of view. It can be seen how the use of the canonical exterior formalism is more adequate and simple because of its manifest covariance in all the steps. The relationship between the form brackets defined in the canonical exterior formalism and the Poisson-brackets is written. Later on, the Dirac-brackets are written by using the second class constraints provided by the canonical exterior formalism. As it can be seen the canonical exterior formalism allows to show how the canonical quantization of the heterotic supersymmetric sigma model is facilitated.