2025/11/03 by Pannell, William H., Ronayne, William Patrick, Stergiou, Andreas · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2511.01971
openalex publication_date 2025/11/03 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28
The gradient property of the renormalisation group (RG) is examined to four-loop order in scalar-fermion systems in d=4 and d=4-ε dimensions. The crucial role played by the beta shift, which is a modification of the standard dim-reg beta function, is elucidated, and specific conditions that it needs to satisfy for the RG flow to be gradient are derived. Over a thousand gradient-flow conditions are found, all of which are scheme-independent and satisfied whenever the full set of results needed to check them is available. It is shown, in the framework of the ε=4-d expansion, that the space of conformal field theories (CFTs) is dominated by those with non-zero beta shift as the number of fields grows. Physical properties of CFTs obtained as solutions where the beta functions are not zero in the ε expansion are discussed.