Study of the Question of an Ultraviolet Zero in the Six-Loop Beta Function of the O($N$) $\lambda |\vec{\varphi }{|}^4$ Theory

Abstract

We study the possibility of an ultraviolet (UV) zero in the six-loop beta function of an O($N$) $\lambda |\vec{\varphi }{|}^4$ field theory in $d=4$ spacetime dimensions. For general $N$, in the range of values of $\lambda$ where a perturbative calculation is reliable, we find evidence against such a UV zero in this six-loop beta function.

15 pages, 1 figure

References in corpus (8)

• A Very Light Dilaton
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• Renormalization-Group Flows and Fixed Points in Yukawa Theories
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• Study of the Six-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory
• Renormalization group functions of ${\varphi }^4$ theory in the MS-scheme to six loops

Cited by in corpus (3)

• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Effect of Scheme Transformations on a Beta Function with Vanishing One-Loop Term
• Study of the Ultraviolet Behavior of an O($N$) $|\vec{\varphi }{|}^6$ Theory in $d=3$ Dimensions