Reference : 2d gauge theories and generalized geometry |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/23195 | |||

2d gauge theories and generalized geometry | |

English | |

Kotov, Alexei [] | |

Salnikov, Vladimir [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Strobl, Thomas [] | |

2014 | |

Journal of High Energy Physics [=JHEP] | |

Institute of Physics Publishing (IOP) | |

Yes (verified by ORBi^{lu}) | |

International | |

1126-6708 | |

1029-8479 | |

Bristol | |

United Kingdom | |

[en] Sigma Models ; Gauge Symmetry ; Differential and Algebraic Geometry | |

[en] 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. | |

http://hdl.handle.net/10993/23195 |

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