Global Gauge Anomalies in Two-Dimensional Bosonic Sigma Models |
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Authors: | Krzysztof Gawȩdzki Rafał R Suszek Konrad Waldorf |
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Institution: | 1.Laboratoire de Physique, C.N.R.S., ENS-Lyon,Université de Lyon,Lyon,France;2.Department Mathematik, Bereich Algebra und Zahlentheorie,Universit?t Hamburg,Hamburg,Germany;3.Department of Mathematics,University of California, Berkeley,Berkeley,USA |
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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. 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. |
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