Sugawara Model, Broken Symmetries, and Massless-Boson Fields

Abstract

It is asserted that the Sugawara theory of currents is equivalent to a canonical Lagranigan theory of massless scalar fields with a Yang-Mills type of interaction. The Sugawara currents are identified with the canonical currents associated with nonlinear transformations of the massless fields. These transformations arise naturally in the context of spontaneous symmetry breakdown. In models of spontaneously broken symmetry in which the symmetry-breaking scalar fields are elementary dynamical variables, that part of the stress-energy tensor containing the Goldstone bosons terms goes over into the Sugawara form when reexpressed in terms of the currents. However, additional terms relating to a massive field appear in the stress-energy tensor, and the massive field operator replaces the usual Sugawara constant. A Sugawara current theory is obtained by eliminating the massive field and retaining the Goldstone boson field only. The reverse is also true in that any Sugawara theory is necessarily equivalent to this canonical representation. Finally, it is shown that if the currents are coupled to gauge fields, a massive Yang-Mills field is obtained.