ZETA-FUNCTION CALCULATION OF THE WEYL DETERMINANT FOR 2-DIMENSIONAL NON-ABELIAN GAUGE-THEORIES IN A CURVED BACKGROUND AND ITS W-Z-W TERMS

Using a cohomological characterization of the consistent and the covariant Lorentz and gauge anomalies, derived from the complexification of the relevant algebras, we study, in d = 2, the definition of the Weyl determinant for a non-Abelian theory with Riemannian background. We obtain two second-order operators that produce, by means of zeta-function regularization, respectively, the consistent and the covariant Lorentz and gauge anomalies, preserving diffeomorphism invariance. We compute exactly their functional determinants and the W-Z-W terms: the 'consistent' determinant agrees with the non-Abelian generalization of the classical Leutwyler's result, while the 'covariant' one gives rise to a covariant version of the usual Wess-Zumino-Witten action.