One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model

Abstract

Recently, a new type of renormalizable ${\varphi }_4^{\star 4}$ scalar model on the Moyal space was proved to be perturbatively renormalizable. It is translation-invariant and introduces in the action a $a/({\theta }^2{p}^2)$ term. We calculate here the $\beta$ and $\gamma$ functions at one-loop level for this model. The coupling constant ${\beta }_{\lambda }$ function is proved to have the same behaviour as the one of the ${\varphi }^4$ model on the commutative ${\mathbb{R}}^4$. The ${\beta }_a$ function of the new parameter $a$ is also calculated. Some interpretation of these results are done.

13 pages, 3 figures

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• Multi-orientable Group Field Theory
• On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review
• Algebraic structures in quantum gravity
• Commutative limit of a renormalizable noncommutative model
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• On Non-Commutative U*(1) Gauge Models and Renormalizability
• Improved Localization of a Renormalizable Non-Commutative Translation Invariant U(1) Gauge Model
• Renormalization of the commutative scalar theory with harmonic term to all orders
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory
• On NCQFT and dimensionless insertions