Critical exponents from five-loop scalar theory renormalization near six-dimensions

Abstract

We present five-loop results for the renormalization of various models with a cubic interaction (in $d=6-2\epsilon$ dimensions). For the scalar model and its $O(n)$-symmetric extension we provide renormalization constants, anomalous dimensions and critical exponents. We discuss in detail the method of calculation, and provide all counterterms up to five loops. This allows one to consider generalizations of the ${\phi }^3$ theory to other symmetries.

10 pages, ancillary files with results

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• Resonant resurgent asymptotics from quantum field theory
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• Ginzburg-Landau Description and Emergent Supersymmetry of the $(3,8)$ Minimal Model
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• The two upper critical dimensions of the Ising and Potts models
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• Sphere free energy of scalar field theories with cubic interactions
• Can effective four-dimensional scalar theory be asymptotically free in a spacetime with extra dimensions?
• Nonextensive percolation and Lee-Yang edge singularity from nonextensive $\lambda {\varphi }^3$ scalar field theory