https://doi.org/10.1140/epjc/s10052-008-0708-1
Regular Article - Theoretical Physics
Color Grosse–Wulkenhaar models: one-loop β-functions
1
International Chair of Mathematical Physics and Applications, ICMPA-UNESCO Chair, Université d’Abomey-Calavi, Cotonou, Benin
2
Faculté des Sciences et Techniques, Université Cheikh Anta Diop, Dakar, Senegal
3
Laboratoire de Physique Théorique, UMR CNRS 8627, Université Paris-Sud X1, 91405, Orsay, France
* e-mail: Vincent.Rivasseau@th.u-psud.fr
** e-mail: vincent.rivasseau@gmail.com
Received:
16
May
2008
Published online:
1
October
2008
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 –
© Springer-Verlag , 2008
