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2d gauge theories and generalized geometry

  • Alexei Kotov
  • Vladimir SalnikovEmail author
  • Thomas Strobl
Open Access
Article

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.

Keywords

Sigma Models Gauge Symmetry Differential and Algebraic Geometry 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Alexei Kotov
    • 1
  • Vladimir Salnikov
    • 2
    Email author
  • Thomas Strobl
    • 3
  1. 1.Department of Mathematics and Statistics, Faculty of Science and TechnologyUniversity of TromsøTromsøNorway
  2. 2.Laboratoire de Mathématiques Nicolas OresmeUniversité de Caen Basse-NormandieCaen CedexFrance
  3. 3.Institut Camille JordanUniversité Claude Bernard Lyon 1Villeurbanne cedexFrance

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