Color Grosse-Wulkenhaar models: One-loop $\beta$-functions

Abstract

The $\beta$-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 asymptotically free in the UV limit for $N>1$, and has a triviality problem or Landau ghost for $N<1$. The vanishing $\beta$-function is recovered solely at N=1. We discuss various possible consequences of these results.

14 pages, 6 Figures

References in corpus (3)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Vacuum configurations for renormalizable non-commutative scalar models
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory

Cited by in corpus (3)

• Duality covariant quantum field theory on noncommutative Minkowski space
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model