Scientific article
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Curved Yang–Mills–Higgs gauge theories in the case of massless gauge bosons

Published inJournal of geometry and physics, vol. 162, 104104
Publication date2021-04

Alexei Kotov and Thomas Strobl have introduced a covariantized formulation of Yang–Mills–Higgs gauge theories whose main motivation was to replace the Lie algebra with Lie algebroids. This allows the introduction of a possibly non-flat connection ∇ on this bundle, after also introducing an additional 2-form ζ in the field strength. We will study this theory in the simplified situation of Lie algebra bundles, i.e.  only massless gauge bosons, and we will provide a physical motivation of ζ . Moreover, we classify ∇ using the gauge invariance, resulting into that ∇ needs to be a Lie derivation law covering a pairing Ξ , as introduced by Mackenzie. There is also a field redefinition, keeping the physics invariant, but possibly changing ζ and the curvature of ∇ . We are going to study whether this can lead to a classical theory, and we will realize that this has a strong correspondence to Mackenzie's study about extending Lie algebroids with Lie algebra bundles. We show that Mackenzie's obstruction class is also an obstruction for having non-flat connections which are not related to a flat connection using the field redefinitions. This class is related to d∇ζ , a tensor which also measures the failure of the Bianchi identity of the field strength and which is invariant under the field redefinition. This tensor will also provide hints about whether ζ can vanish after a field redefinition.

  • Classical field theory
  • Lie groups and Lie (super)algebras
  • Symplectic geometry
  • Mathematical gauge theory
  • Differential geometry
  • High energy physics — theory
  • Mathematical physics
  • algebra: Lie
  • gauge boson: massless
  • invariance: gauge
  • field strength
  • Bianchi identity
  • curvature
  • Yang-Mills-Higgs theory
  • covariance
  • fibre bundle
Note36 pages (including title page and five pages of the appendix)
Citation (ISO format)
FISCHER, Simon-Raphaël. Curved Yang–Mills–Higgs gauge theories in the case of massless gauge bosons. In: Journal of geometry and physics, 2021, vol. 162, p. 104104. doi: 10.1016/j.geomphys.2021.104104
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Article (Published version)
ISSN of the journal0393-0440

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Creation10/15/2021 9:31:00 PM
First validation10/15/2021 9:31:00 PM
Update time03/16/2023 1:31:28 AM
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