  We study the Abelian Thirring Model when the fermionic fields have
non-conserved chiral charge: $\Delta {\cal Q}_5 =N$. One of the main features
we find for this model is the dependence of the Virasoro central charge on both
the Thirring coupling constant and $N$. We show how to evaluate correlation
functions and in particular we compute the conformal dimensions for fermions
and fermionic bilinears, which depend on the fermionic chiral charge. Finally
we build primary fields with arbitrary conformal weight.
