CONSERVATION LAWS AND GEOMETRY OF PERTURBED COSET MODELS

Abstract

We present a Lagrangian description of the SU(2)/U(1) coset model perturbed by its first thermal operator. This is the simplest perturbation that changes sign under Krammers-Wannier duality. The resulting theory, which is a two-component generalization of the sine-Gordon model, is then taken in Minkowski space. For negative values of the coupling constant g, it is classically equivalent to the O(4) nonlinear σ model reduced in a certain frame. For g>0, it describes the relativistic motion of vortices in a constant external field. Viewing the classical equations of motion as a zero curvature condition, we obtain recursive relations for the infinitely many conservation laws by the abelianization method of gauge connections. The higher spin currents are constructed entirely using an off-critical generalization of the W∞ generators. We give a geometric interpretation to the corresponding charges in terms of embeddings. Applications to the chirally invariant U(2) Gross-Neveu model are also discussed.