Leibniz-Yang-Mills Gauge Theories and the 2-Higgs Mechanism
| Autor: | Thomas Strobl |
|---|---|
| Přispěvatelé: | Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
Leibniz algebra split [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] FOS: Physical sciences Yang–Mills existence and mass gap differential forms algebra: Lie Type (model theory) 01 natural sciences Computer Science::Digital Libraries Gauge Field Theories symbols.namesake High Energy Physics::Theory 0103 physical sciences Lie algebra Gauge theory 010306 general physics Mathematical Physics Gauge symmetry Mathematical physics Physics 010308 nuclear & particles physics [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] symmetry: gauge mathematical methods Mathematical Physics (math-ph) space Beyond the standard model Bracket (mathematics) High Energy Physics - Theory (hep-th) gauge field theory: Yang-Mills Gauge Symmetry symbols Higgs mechanism Leibniz |
| Zdroj: | Phys.Rev.D Phys.Rev.D, 2019, 99 (11), pp.115026. ⟨10.1103/PhysRevD.99.115026⟩ Physical Review Physical Review D Physical Review D, American Physical Society, 2019, 99 (11), pp.115026. ⟨10.1103/PhysRevD.99.115026⟩ |
| ISSN: | 1550-7998 1550-2368 |
| DOI: | 10.1103/PhysRevD.99.115026⟩ |
| Popis: | A quadratic Leibniz algebra $(\mathbb{V},[ \cdot, \cdot ],\kappa)$ gives rise to a canonical Yang-Mills type functional $S$ over every space-time manifold. The gauge fields consist of 1-forms $A$ taking values in $\mathbb{V}$ and 2-forms $B$ with values in the subspace $\mathbb{W} \subset \mathbb{V}$ generated by the symmetric part of the bracket. If the Leibniz bracket is anti-symmetric, the quadratic Leibniz algebra reduces to a quadratic Lie algebra, $B\equiv 0$, and $S$ becomes identical to the usual Yang-Mills action functional. We describe this gauge theory for a general quadratic Leibniz algebra. We then prove its (classical and quantum) equivalence to a Yang-Mills theory for the Lie algebra ${\mathfrak{g}} = \mathbb{V}/\mathbb{W}$ to which one couples massive 2-form fields living in a ${\mathfrak{g}}$-representation. Since in the original formulation the B-fields have their own gauge symmetry, this equivalence can be used as an elegant mass-generating mechanism for 2-form gauge fields, thus providing a 'higher Higgs mechanism' for those fields. Comment: 6 pages; a subsection with remarks on finite gauge transformations added. Version to be published in Phys. Rev. D |
| Databáze: | OpenAIRE |
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