Running coupling in SU(2) gauge theory with two adjoint fermions

TL;DR

This study investigates the running coupling and fixed point behavior of SU(2) gauge theory with two adjoint fermions on the lattice, providing insights into its nonperturbative dynamics and anomalous dimensions.

Contribution

It extends previous lattice studies by using improved actions at larger couplings to explore the fixed point and anomalous dimension in SU(2) gauge theory with adjoint fermions.

Findings

Evidence for a fixed point in the coupling range 2.2 to 3.

Measured anomalous dimension at the fixed point is approximately 0.2.

Discretization effects are significant at weak coupling, complicating continuum extrapolation.

Abstract

We study SU(2) gauge theory with two Dirac fermions in the adjoint representation of the gauge group on the lattice. Using clover improved Wilson fermion action with hypercubic truncated stout smearing we perform simulations at larger coupling than earlier. We measure the evolution of the coupling constant using the step scaling method with Schr\"odinger functional and study the remaining discretization effects. At weak coupling we observe significant discretization effects, which make it difficult to obtain a fully controlled continuum limit. Nevertheless, the data remains consistent with the existence of a fixed point in the interval $2.2\lesssim g^{\ast 2}\lesssim 3$. We also measure the anomalous dimension and find its value at the fixed point is $\gamma^\ast\simeq 0.2\pm 0.03$.