Aspects of Non-Abelian Toda Theories

Abstract

We present a definition of the non-abelian generalisations of affine Toda theory related from the outset to vertex operator constructions of the corresponding Kac-Moody algebra $\gh$. Reuslts concerning conjugacy classes of the Weyl group of the finite Lie algebra $\fing$ to embeddings of $A_1$ in $\fing$ are used both to present the theories, and to elucidate their soliton spectrum. We confirm the conjecture of \cite{OSU93} for the soliton specialisation of the Leznov-Saveliev solution. The energy-momentum tensor of such theories is shown to split into a total derivative part and a part dependent only on the free fields which appear in the general solution, and vanish for the soliton solutions. Analogues are provided of the results known for the classical solitons of abelian Toda theories.