Perturbative running of the twisted Yang-Mills coupling in the gradient flow scheme

TL;DR

This paper discusses a perturbative approach to compute the running of the Yang-Mills coupling using gradient flow with twisted boundary conditions, aiming to determine the scheme's mbda parameter.

Contribution

It introduces a novel perturbative expansion of the Yang-Mills energy density with twisted boundary conditions up to fourth order, advancing the understanding of the coupling's running in this scheme.

Findings

Reproduced the universal coefficient of the 1/ε term in dimensional regularisation.

Performed a perturbative expansion up to fourth order in the coupling.

Ongoing work to determine the mbda parameter from finite parts.

Abstract

We report on our ongoing computation of the perturbative running of the Yang-Mills coupling using gradient flow techniques. In particular, we use the gradient flow method with twisted boundary conditions to perform a perturbative expansion of the expectation value of the Yang-Mills energy density up to fourth order in the coupling at finite flow time. We regularise the resulting integrals using dimensional regularisation, and reproduce the universal coefficient of the 1/{\epsilon} term in the relation between bare and renormalised couplings. The computation of the finite part leading to a determination of the {\Lambda} parameter in this scheme is underway.