Bootstrapping non-commutative gauge theories from L algebras

  • Ralph Blumenhagen
  • Ilka Brunner
  • Vladislav Kupriyanov
  • Dieter Lüst
Open Access
Regular Article - Theoretical Physics


Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L algebra. The appearance of a non-trivial A algebra is discussed, as well.


Non-Commutative Geometry D-branes Gauge Symmetry 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Ralph Blumenhagen
    • 1
  • Ilka Brunner
    • 2
  • Vladislav Kupriyanov
    • 1
    • 3
    • 4
  • Dieter Lüst
    • 1
    • 2
  1. 1.Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)MünchenGermany
  2. 2.Arnold Sommerfeld Center for Theoretical PhysicsLMUMünchenGermany
  3. 3.CMCC-Universidade Federal do ABCSanto AndréBrazil
  4. 4.Tomsk State UniversityTomskRussia

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