GAUGING OF LORENTZ GROUP WZW MODEL BY ITS NULL SUBGROUP

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 th at we interpret as a Liouville field. By gauging a boosted SO(3) subgr oup, we find that in the limit of the large boost. the theory can be i nterpreted 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.