Global gauge anomalies in two-dimensional bosonic sigma models

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.

50 pages, 1 figure

References in corpus (16)

• Doubled Geometry and T-Folds
• WZW branes and gerbes
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories
• Simple currents versus orbifolds with discrete torsion -- a complete classification
• The resolution of field identification fixed points in diagonal coset theories
• Unoriented WZW Models and Holonomy of Bundle Gerbes
• Abelian and non-Abelian branes in WZW models and gerbes
• Basic gerbe over non simply connected compact groups
• Gauged Wess-Zumino terms and Equivariant Cohomology
• Higher bundle gerbes and cohomology classes in gauge theories
• Global Aspects Of Gauged Wess-Zumino-Witten Models
• Gauging the Wess-Zumino term of a sigma model with boundary
• Maverick Examples Of Coset Conformal Field Theories
• Polyakov-Wiegmann Formula and Multiplicative Gerbes
• WZW orientifolds and finite group cohomology

Cited by in corpus (9)

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• A higher stacky perspective on Chern-Simons theory
• Black hole microstates from the worldsheet
• Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
• Dirac Sigma Models from Gauging
• Square root of gerbe holonomy and invariants of time-reversal-symmetric topological insulators
• The gauging of two-dimensional bosonic sigma models on world-sheets with defects
• Global gauge anomalies in coset models of conformal field theory
• Gerbes in Geometry, Field Theory, and Quantisation