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The European Physical Journal C

, Volume 58, Issue 1, pp 115–122 | Cite as

Color Grosse–Wulkenhaar models: one-loop β-functions

  • Joseph Ben Geloun
  • Vincent RivasseauEmail author
Regular Article - Theoretical Physics

Abstract

The β-functions of O(N) and U(N) invariant Grosse–Wulkenhaar models are computed at one loop using the matrix basis. In particular, for “parallel interactions”, the model is proved to be asymptotically free in the UV limit for N>1, and it has a triviality problem or Landau ghost for N<1. The vanishing β-function is recovered solely at N=1. We discuss various possible consequences of these results.

PACS

02.40.Gh 11.10.Nx 

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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2008

Authors and Affiliations

  1. 1.International Chair of Mathematical Physics and Applications, ICMPA-UNESCO ChairUniversité d’Abomey-CalaviCotonouBenin
  2. 2.Faculté des Sciences et TechniquesUniversité Cheikh Anta DiopDakarSenegal
  3. 3.Laboratoire de Physique Théorique, UMR CNRS 8627Université Paris-Sud X1OrsayFrance

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