Gauging of Lorentz Group Wzw Model by Its Null Subgroup

We consider the standard vector gauging of Lorentz group SO(3, 1) WZWmodel 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 it as a Liouville field. Gauging a boosted SO(3) subgroup, we find that in the limit of the large boost, the theory can be interpreted as an interacting Toda theory. We also take the generalized non-standard bilinear form for SO(3, 1) and gauge both SO(3) and E(2) subgroups and discuss the the resultant theories. e-mail address: [email protected]