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 (20)

• Noncommutative Field Theory
• Background Independent Quantum Gravity: A Status Report
• Quantum Field Theory on Noncommutative Spaces
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Group Field Theory: An overview
• Lectures on Loop Quantum Gravity
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Power-counting theorem for non-local matrix models and renormalisation
• The β-function in duality-covariant noncommutative ϕ^4-theory
• Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space
• Renormalization of noncommutative phi 4-theory by multi-scale analysis
• Non-commutative Renormalization
• Vacuum configurations for renormalizable non-commutative scalar models
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Renormalisation of ϕ^4-theory on noncommutative R^4 to all orders
• Parametric Representation of Noncommutative Field Theory
• Noncommutative Field Theory and Spontaneous Symmetry Breaking
• Renormalization of the Orientable Non-commutative Gross-Neveu Model
• Noncommutative Linear Sigma Models

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