Six-loop beta functions in general scalar theory

Abstract

We consider general renormalizable scalar field theory and derive six-loop beta functions for all parameters in d = 4 dimensions within the $\overline{MS}$-scheme. We do not explicitly compute relevant loop integrals but utilize $O(n)$-symmetric model counter-terms available in the literature. We consider dimensionless couplings and parameters with a mass scale, ranging from the trilinear self-coupling to the vacuum energy. We use obtained results to extend renormalization-group equations for several vector, matrix, and tensor models to the six-loop order. Also, we apply our general expressions to derive new contributions to beta functions and anomalous dimensions in the scalar sector of the Two-Higgs-Doublet Model.

25 pages, matches published version, results in ancillary files

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• On Ambiguities and Divergences in Perturbative Renormalization Group Functions
• CFTs with $U(m)\times U(n)$ Global Symmetry in 3D and the Chiral Phase Transition of QCD
• Towards general scalar-Yukawa renormalisation group equations at three-loop order
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Six-loop $\epsilon$ expansion of three-dimensional $\text{U}(n)\times \text{U}(m)$ models
• Six-loop anomalous dimension of the ${\varphi }^Q$ operator in the $O(N)$ symmetric model
• The tricritical Ising CFT and conformal bootstrap
• Critical behavior of isotropic systems with strong dipole-dipole interaction: three-loop study
• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• Bi- and tetracritical phase diagrams in three dimensions
• Anomalous Dimensions in Hypercubic Theories
• Asymptotic safety in the Litim-Sannino model at four loops
• Effective potential in leading logarithmic approximation in non-renormalisable $SO(N)$ scalar field theories
• Classifying irreducible fixed points of five scalar fields in perturbation theory
• Critical exponents of model with matrix order parameter from resummation of six-loop results for anomalous dimensions
• Superfluidity in multicomponent fermions via the functional renormalization group
• Conformal Windows beyond Asymptotic Freedom
• Fluctuation-induced first-order superfluid transition in unitary $\mathrm{SU}(N)$ Fermi gases