Critical dimensions of spinning strings on group manifolds from Fujikawa’s method

A. Eastaugh; L. Mezincescu; E. Sezgin; P. van Nieuwenhuizen

doi:10.1103/PhysRevLett.57.29

Critical dimensions of spinning strings on group manifolds from Fujikawa’s method

A. Eastaugh, L. Mezincescu, E. Sezgin, and P. van Nieuwenhuizen

Phys. Rev. Lett. 57, 29 – Published 7 July 1986

Abstract

We discuss the derivation of Fujikawa’s 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.