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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Cited by in corpus (3)

• Commutative limit of a renormalizable noncommutative model
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Improved Localization of a Renormalizable Non-Commutative Translation Invariant U(1) Gauge Model