  An analysis is given of the structure of a general two-dimensional Toda field
theory involving bosons and fermions which is defined in terms of a set of
simple roots for a Lie superalgebra. It is shown that a simple root system for
a superalgebra has two natural bosonic root systems associated with it which
can be found very simply using Dynkin diagrams; the construction is closely
related to the question of how to recover the signs of the entries of a Cartan
matrix for a superalgebra from its Dynkin diagram. The significance for Toda
theories is that the bosonic root systems correspond to the purely bosonic
sector of the integrable model, knowledge of which can determine the bosonic
part of the extended conformal symmetry in the theory, or its classical mass
spectrum, as appropriate. These results are applied to some special kinds of
models and their implications are investigated for features such as
supersymmetry, positive kinetic energy and generalized reality conditions for
the Toda fields. As a result, some new families of integrable theories with
positive kinetic energy are constructed, some containing a mixture of massless
and massive degrees of freedom, others being purely massive and supersymmetric,
involving a number of coupled sine/sinh-Gordon theories.
