The SU(N) running coupling in the twisted gradient flow scheme and volume independence

TL;DR

This paper investigates the SU(N) Yang-Mills theory's running coupling using the twisted gradient flow scheme, focusing on volume independence and finite volume effects across different gauge groups and lattice sizes.

Contribution

It introduces a method to reduce finite volume effects via twisted boundary conditions and tests volume independence in the TGF scheme across various SU(N) groups.

Findings

Finite volume effects are reduced with twisted boundary conditions.

The effective size in the twisted plane combines the number of colours and torus period.

Results support volume independence in the studied scheme.

Abstract

We report on an ongoing study of the running coupling of SU(N) pure Yang-Mills theory in the twisted gradient flow scheme (TGF). The study exploits the idea that twisted boundary conditions reduce finite volume effects, leading to an effective size in the twisted plane that combines the number of colours and the torus period. We test this hypothesis by computing the TGF running coupling and the SU(N) $\Lambda-$ parameter on asymmetric lattices of size $(NL)^2L^2$ for various gauge groups. Finite volume effects are monitored by analyzing the coupling in different planes and by comparing results at different number of colours.