Scalar-fermion fixed points in the ε expansion

• Published in: The journal of high energy physics Vol. 2023; no. 8; pp. 128 - 47
• Main Authors: Pannell, William H., Stergiou, Andreas
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2023; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Couplings; Eigenvalues; Elementary Particles; Fermions; Fixed points (mathematics); High energy physics; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Renormalization and Regularization; Renormalization Group; Scalars; Scale and Conformal Symmetries; String Theory; Symmetry; Scale and Conformal Symmetries; Renormalization Group; Renormalization and Regularization
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2023)128

A bstract The one-loop beta functions for systems of N s scalars and N f fermions interacting via a general potential are analysed as tensorial equations in 4 − ε dimensions. Two distinct bounds on combinations of invariants constructed from the couplings are derived and, subject to an assumption, are used to prove that at one-loop order the anomalous dimensions of the elementary fields are universally restricted by γ ϕ ⩽ 1 2 N s ε and γ ψ ⩽ N s ε . For each root of the Yukawa beta function there is a number of roots of the quartic beta function, giving rise to the concept of ‘levels’ of fixed points in scalar-fermion theories. It is proven that if a stable fixed point exists within a certain level, then it is the only such fixed point at that level. Solving the beta function equations, both analytically and numerically, for low numbers of scalars and fermions, well-known and novel fixed points are found and their stability properties are examined. While a number of fixed points saturate one out of the two bounds, only one fixed point is found which saturates both of them.