  The renormalization of the topological term in the two-dimensional nonlinear
O(3) model is studied by means of the Functional Renormalization Group. By
considering the topological charge as a limit of a more general operator, it is
shown that a finite multiplicative renormalization occurs in the extreme
infrared. In order to compute the effects of the zero modes, a specific
representation of the Clifford algebra is developed which allows to reformulate
the bosonic problem in terms of Dirac operators and to employ the index
theorem.
