The gradient flow running coupling with twisted boundary conditions

TL;DR

This paper investigates the gradient flow method for defining a running coupling in Yang-Mills theories with twisted boundary conditions, demonstrating its effectiveness and precision in non-perturbative $SU(2)$ gauge studies.

Contribution

It introduces a new approach using twisted boundary conditions for the gradient flow running coupling, showing its advantages in lattice simulations.

Findings

Non-perturbative $SU(2)$ coupling running measured.

Technique exhibits mild cutoff effects.

High numerical precision achieved in simulations.

Abstract

We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $\langle E(t)\rangle$ is used to define a running coupling at a scale given by the linear size of the finite volume box. We compute the non-perturbative running of the pure gauge $SU(2)$ coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations. We also comment on the inclusion of matter fields.