SOLITONS AND THE ENERGY-MOMENTUM TENSOR FOR AFFINE TODA THEORY

Following Leznov and Saveliev, we present the general solution to Toda field theories of conformal, affine or conformal affine type, associa ted with a simple Lie algebra g. These depend on a free massless field and on a group element. By putting the former to zero, soliton soluti ons to the affine Toda theories with imaginary coupling constant resul t with the soliton data encoded in the group element. As this requires a reformulation of the affine Kac-Moody algebra closely related to th at already used to formulate the physical properties of the particle e xcitations, including their scattering matrices, a unified treatment o f particles and solitons emerges. The physical energy-momentum tensor for a general solution is broken into a total derivative plus a part d ependent only on the derivatives of the free field. Despite the non-li nearity of the field equations and their complex nature the energy and momentum of the N-soliton solution is shown to be real, equalling the sum of contributions from the individual solitons. There are rank-g s pecies of soliton, with masses given by a generalisation of a formula due to Hollowood, being proportional to the components of the left Per ron-Frobenius eigenvector of the Cartan matrix of g.