EXACT LORENTZ ANOMALY IN TWO DIMENSIONS

The perturbative computation of the gravitational anomaly in curved space–time and in 1+1 dimensions is considered. This determination is obtained by a known method of complexification of the action variables applied to the fermionic effective action. Our result gives an exact definition of the Lorentz anomaly and it is introductory to a nonambiguous nonperturbative determination of the gravitational anomaly on curved manifolds. The quantum variation of the effective action, or Weyl determinant, is regularized with the help of the ζ-function technique, by extending the local algebra of infinitesimal current generators to complex values. Some ambiguities in the definition and computation of gauge anomalies are hopefully clarified.