Global gauge anomalies in twodimensional bosonic sigma models
Abstract
We revisit the gauging of rigid symmetries in twodimensional bosonic sigma models with a WessZumino term in the action. Such a term is related to a background closed 3form H on the target space. More exactly, the sigmamodel Feynman amplitudes of classical fields are associated to a bundle gerbe with connection of curvature H over the target space. Under conditions that were unraveled more than twenty years ago, the classical amplitudes may be coupled to the topologically trivial gauge fields of the symmetry group in a way which assures infinitesimal gauge invariance. We show that the resulting gauged WessZumino amplitudes may, nevertheless, exhibit global gauge anomalies that we fully classify. The general results are illustrated on the example of the WZW and the coset models of conformal field theory. The latter are shown to be inconsistent in the presence of global anomalies. We introduce a notion of equivariant gerbes that allow an anomalyfree coupling of the WessZumino amplitudes to all gauge fields, including the ones in nontrivial principal bundles. The obstructions to the existence of equivariant gerbes and their classification are discussed. The choice of different equivariant structures on the same bundle gerbe gives rise to a new type of discretetorsion ambiguities in the gauged amplitudes. An explicit construction of gerbes equivariant with respect to the adjoint symmetries over compact simply connected simple Lie groups is given.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 arXiv:
 arXiv:1003.4154
 Bibcode:
 2010arXiv1003.4154G
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 50 pages, 1 figure