2023/05/23 by William H. Pannell, Pannell, William H., Andreas Stergiou +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el #hep-th
paper · pdf · doi:10.48550/arxiv.2305.14417
49 pages, 20 figures, 10 tables. v2 corrected figures and added comments. v3 expanded discussion, and accepted for publication in JHEP. v4 typos corrected
arxiv created 2026/07/31 · arxiv updated 2026/08/03
The one-loop beta functions for systems of Ns scalars and Nf 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 γϕ≤(1)/(2)Ns ε and γψ≤ Ns 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.