2d gauge theories and generalized geometry

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


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.


Sigma Models Gauge Symmetry Differential and Algebraic Geometry 


Open Access

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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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