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

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.

Comments: 7 pages, no figures, contribution to the 34th International Symposium on Lattice Field Theory, 24-30 July 2016, Southampton, UK