We discuss the derivation of Fujikawas method of the critical dimensions of the following models: the bosonic and N=1 locally supersymmetric nonlinear sigma models, and the N=2 and N=4 spinning strings. We argue that in the N=1 models the group-invariant measure is supersymmetric and does not lead to an extra anomaly. Our results are consistent with conjectured non-Abelian bosonization formulas for gravitational path integrals only for k=1, where k is the central extension of the Kac-Moody algebra.
ASJC Scopus subject areas
- Physics and Astronomy(all)