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Article Dans Une Revue Journal of High Energy Physics Année : 2014

2d gauge theories and generalized geometry

Alexei Kotov
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Résumé

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" TM ≡ T M ⊕ T * 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 ⊂ TM (or, more generally, the choide of a "small Dirac-Rinehart sheaf" 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 × g → M into D → M (or the algebraic analogue of the morphism in the case of 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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Dates et versions

hal-02403727 , version 1 (11-12-2019)

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Alexei Kotov, Vladimir Salnikov, Thomas Strobl. 2d gauge theories and generalized geometry. Journal of High Energy Physics, 2014, 2014 (8), ⟨10.1007/JHEP08(2014)021⟩. ⟨hal-02403727⟩
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