General Four-Loop Beta Function for Scalar-Fermion Theories in Three Dimensions

2025/12/01 by Schröder, York, Stamou, Emmanuel, Steudtner, Tom +1 · 2 citations
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2512.02123

Abstract

We present general four-loop template β-functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing N=1 and N=2 supersymmetry, we obtain relations between the template RGE coefficients, valid in any renormalisation scheme. Directly in d=3, we identify a new theory with a non-trivial IR fixed point that is under perturbative control in a large-N limit. We provide up-to-date numerical results for all required massive tadpole master integrals up to four loops and complement them with analytic expressions where available.

Citations

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Related

• Four Loop Renormalisation Group Equations in general Gross-Neveu-Yukawa Theories
• Explorations in Scalar Fermion Theories: β-functions, Supersymmetry and Fixed Points
• General Quartic β-Function at Three Loops
• Scheme Dependence and Multiple Couplings
• beta-functions in higher dimensional field theories