2014/11/30 by I. Jack, C. Poole · 31 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Consistency (knowledge bases) #Dimension (graph theory) #Fermion #Gauge (firearms) #Gauge anomaly #Gauge theory #Introduction to gauge theory #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Quantum field theory #Supersymmetric gauge theory #hep-th
paper · pdf · doi:10.1007/jhep01(2015)138
published in Journal of High Energy Physics 2015(1) (Springer Nature) · 28 pages; uses axodraw; typos corrected, also some sign errors corrected in Sect 5
openalex publication_date 2015/01/01 · openalex created_date 2016/06/24 · arxiv created 2017/07/26 · arxiv updated 2017/07/27 · openalex updated_date 2026/08/05
The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the β-functions via a gradient flow equation involving a positive definite metric. We construct the a-function at four-loop order for a general gauge theory with fermions and scalars, using only one and two loop β-functions; we are then able to provide a stringent consistency check on the general three-loop gauge β-function. In the case of an N=1 supersymmetric gauge theory, we present a general condition on the chiral field anomalous dimension which guarantees an exact all-orders expression for the a-function; and we verify this up to fifth order (corresponding to the three-loop anomalous dimension).