2d gauge theories and generalized geometry

Abstract

We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra g leads naturally to the appearance of the “generalized tangent bundle” \( \mathbb{T} \) MTMT * M by means of composite fields. Gauge transformations of the composite fields follow the Courant bracket, closing upon the choice of a Dirac structure D\( \mathbb{T} \) M (or, more generally, the choide of a “small Dirac-Rinehart sheaf” \( \mathcal{D} \)), in which the fields as well as the symmetry parameters are to take values. In these new variables, the gauge theory takes the form of a (non-topological) Dirac sigma model, which is applicable in a more general context and proves to be universal in two space-time dimensions: a gauging of g of a standard sigma model with Wess-Zumino term exists, iff there is a prolongation of the rigid symmetry to a Lie algebroid morphism from the action Lie algebroid M × \( \mathfrak{g} \)M into DM (or the algebraic analogue of the morphism in the case of \( \mathcal{D} \)). The gauged sigma model results from a pullback by this morphism from the Dirac sigma model, which proves to be universal in two-spacetime dimensions in this sense.

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Correspondence to Vladimir Salnikov.

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ArXiv ePrint: 1407.5439

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Kotov, A., Salnikov, V. & Strobl, T. 2d gauge theories and generalized geometry. J. High Energ. Phys. 2014, 21 (2014). https://doi.org/10.1007/JHEP08(2014)021

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Keywords

  • Sigma Models
  • Gauge Symmetry
  • Differential and Algebraic Geometry