Gauging the Wess-Zumino term of a sigma model with boundary

Abstract

We investigate the gauging of the Wess-Zumino term of a sigma model with boundary. We derive a set of obstructions to gauging and we interpret them as the conditions for the Wess-Zumino term to extend to a closed form in a suitable equivariant relative de Rham complex. We illustrate this with the two-dimensional sigma model and we show that the new obstructions due to the boundary can be interpreted in terms of Courant algebroids. We specialise to the case of the Wess-Zumino-Witten model, where it is proved that there always exist suitable boundary conditions which allow gauging any subgroup which can be gauged in the absence of a boundary. We illustrate this with two natural classes of gaugings: (twisted) diagonal subgroups with boundary conditions given by (twisted) conjugacy classes, and chiral isotropic subgroups with boundary conditions given by cosets.

arXiv comment18 pages (minor changes in response to referee report)

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• Black hole microstates from the worldsheet
• Courant-like brackets and loop spaces
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• Topological Field Theories induced by twisted R-Poisson structure in any dimension
• The Structure of Non-Abelian Kinks
• Global gauge anomalies in two-dimensional bosonic sigma models
• Wrapped Fivebranes Redux
• The BV action of 3D twisted R-Poisson sigma models
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• Towards a quadratic Poisson algebra for the subtracted classical monodromy of Symmetric Space Sine-Gordon theories
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