  Consider a manifold endowed with the action of a Lie group. We study the
relation between the cohomology of the Cartan complex and the equivariant
cohomology by using the equivariant De Rham complex developed by Getzler, and
we show that the cohomology of the Cartan complex lies on the 0-th row of the
second page of a spectral sequence converging to the equivariant cohomology. We
use this result to generalize a result of Witten on the equivalence of absence
of anomalies in gauge WZW actions on compact Lie groups to the existence of
equivariant extension of the WZW term, to the case on which the gauge group is
the special linear group with real coefficients.
