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Global gauge anomalies in two-dimensional bosonic sigma models | | Krzysztof Gawedzki
; Rafal R. Suszek
; Konrad Waldorf
; | | Date: |
22 Mar 2010 | | Abstract: | We revisit the gauging of rigid symmetries in two-dimensional bosonic sigma
models with a Wess-Zumino term in the action. Such a term is related to a
background closed 3-form H on the target space. More exactly, the sigma-model
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
Wess-Zumino 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 anomaly-free coupling of the Wess-Zumino
amplitudes to all gauge fields, including the ones in non-trivial 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 discrete-torsion 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. | | Source: | arXiv, 1003.4154 | | Services: | Forum | Review | PDF | Favorites | |
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