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We consider the standard vector gauging of Lorentz group SO$(3,1)$
WZW model by
its non-semisimple null Euclidean subgroup in two dimensions $E(2)$. The
resultant effective action of the theory is seen to describe a one-dimensional
bosonic field in the presence of external charge that we interpret as a
Liouville field. By gauging a boosted SO$(3)$ subgroup, we find that in the
limit of the large boost, the theory can be intrepreted as an interacting Toda
theory. We take also the generalized nonstandard bilinear
form for SO$(3,1)$ and gauge both SO$(3)$ and $E(2)$ subgroups and
discuss the resultant theories.
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