2019/06/30 by Colin Poole, Anders Eller Thomsen · 1 citation
Physics and Astronomy · #hep-th #hep-ph
paper · pdf · doi:10.1007/jhep09(2019)055
63 pages, 11 figures. Version 2 includes 2 ancillary files that should have been uploaded in the first place. Version 3 corrects typos and provides slight clarifications in some places
arxiv created 2019/08/27 · arxiv updated 2019/10/02
The β-functions of marginal couplings are known to be closely related to the A -function through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the β-functions by parametrizing the terms in Osborn's equation as polynomials in the couplings, then eliminating unknown A and TIJ coefficients. In this paper we extend this program to completely general gauge theories with arbitrarily many Abelian and non-Abelian factors. We detail the computational strategy used to extract consistency conditions on β-functions, and discuss our automation of the procedure. Finally, we implement the procedure up to 4-, 3-, and 2-loops for the gauge, Yukawa and quartic couplings respectively, corresponding to the present forefront of general β-function computations. We find an extensive collection of highly non-trivial constraints, and argue that they constitute an useful supplement to traditional perturbative computations; as a corollary, we present the complete 3-loop gauge β-function of a general QFT in the MS scheme, including kinetic mixing.