  We consider the relation between affine Toda field theories (ATFT) and
Landau-Ginzburg Lagrangians as alternative descriptions of deformed 2d CFT.
First, we show that the two concrete implementations of the deformation are
consistent once quantum corrections to the Landau-Ginzburg Lagrangian are taken
into account. Second, inspired by Gepner's fusion potentials, we explore the
possibility of a direct connection between both types of Lagrangians; namely,
whether they can be transformed one into another by a change of variables. This
direct connection exists in the one-variable case, namely, for the sine-Gordon
model, but cannot be established in general. Nevertheless, we show that both
potentials exhibit the same structure of extrema.
