Determining the conformal window: SU(2) gauge theory with N_f = 4, 6 and 10 fermion flavours

TL;DR

This study investigates the infrared behavior of SU(2) gauge theories with 4, 6, and 10 fermion flavors on the lattice, identifying QCD-like behavior at four flavors and a possible fixed point at ten flavors, with inconclusive results at six flavors.

Contribution

It provides lattice measurements of the running coupling and mass anomalous dimension near the conformal window edges for SU(2) gauge theories with multiple fermion flavors.

Findings

At Nf=4, the coupling grows in the infrared, indicating QCD-like behavior.

At Nf=10, results suggest the presence of an infrared fixed point.

At Nf=6, the coupling evolution slows but remains inconclusive.

Abstract

We study the evolution of the coupling in SU(2) gauge field theory with $N_f=4$, 6 and 10 fundamental fermion flavours on the lattice. These values are chosen close to the expected edges of the conformal window, where the theory possesses an infrared fixed point. We use improved Wilson-clover action, and measure the coupling in the Schr\"odinger functional scheme. At four flavours we observe that the couping grows towards the infrared, implying QCD-like behaviour, whereas at ten flavours the results are compatible with a Banks-Zaks type infrared fixed point. The six flavour case remains inconclusive: the evolution of the coupling is seen to become slower at the infrared, but the accuracy of the results falls short from fully resolving the fate of the coupling. We also measure the mass anomalous dimension for the $N_f=6$ case.