TY - JOUR
T1 - Constraints on 3- and 4-loop β-functions in a general four-dimensional Quantum Field Theory
AU - Poole, Colin
AU - Thomsen, Anders Eller
PY - 2019/9
Y1 - 2019/9
N2 - 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 à 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 M S ¯ scheme, including kinetic mixing.
AB - 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 à 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 M S ¯ scheme, including kinetic mixing.
KW - Gauge Symmetry
KW - Renormalization Group
U2 - 10.1007/JHEP09(2019)055
DO - 10.1007/JHEP09(2019)055
M3 - Journal article
AN - SCOPUS:85072997602
VL - 2019
JO - Journal of High Energy Physics (Online)
JF - Journal of High Energy Physics (Online)
SN - 1126-6708
IS - 9
M1 - 55
ER -