Abstract
Results are reported for the β-function of weakly coupled conformal gauge theories on the lattice, SU(3) with Nf = 14 fundamental and Nf = 3 sextet fermions. The models are chosen to be close to the upper end of the conformal window where perturbation theory is reliable hence a fixed point is expected. The study serves as a test of how well lattice methods perform in the weakly coupled conformal cases. We also comment on the 5-loop β-function of two models close to the lower end of the conformal window, SU(3) with Nf = 12 fundamental and Nf = 2 sextet fermions.
Highlights
We study gauge theories inside the conformal window close to its upper end
We study here the weakly coupled conformal case which can be tested on the lattice with predictable and controlled results in sufficient orders of perturbation theory
Studies of gauge theories close to the lower end of conformal window are plaqued by large systematic effects
Summary
We study gauge theories inside the conformal window close to its upper end. In this region the gauge group, number of massless fermion flavors and the representation they carry are such that the perturbative β-function possesses a fixed point at a small value of the renormalized coupling. In principle lattice simulations are an ideal tool to determine whether a given model is inside or outside the conformal window exactly because the lattice setup can capture all non-perturbative effects. Systematic effects can be large sometimes leading to controversies for models close to the lower end of the conformal window. In this work the finite volume gradient flow [4] running coupling scheme [5, 6] is used to calculate the β-function and to probe the infrared dynamics
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