Global anomalies in canonical gravity

Abstract

In this note we study the structure of diffeomorphism anomalies in 3 + 1 canonical gravity coupled to a chiral massless fermion. We find that when the spatial manifold Σ is S 3 or a Lens space L( p, q), the first homotopy group of the related diffeomorphism group can be non-trivial and hence the question of global anomalies becomes relevant. Here we show that for gravity coupled to SU(2) chiral fermions, assuming the strong form of the Hatcher conjecture, SU(2)-induced diffeomorphism anomalies do not occur whenever Σ is S 3 or a Lens space.