The perturbative SU(N) one-loop running coupling in the twisted gradient flow scheme

We report on our computation of the perturbative running of the 't Hooft coupling in a pure gauge $SU(N)$ theory with twisted boundary conditions. The coupling is defined in terms of the energy density of the flow fields at a scale given by a particular combination of the linear size of the torus and the rank of the gauge group. We present our results for the matching at one-loop order to the $\bar{MS}$ scheme in the case of a two-dimensional non-trivial twist. The ratio of $\Lambda$ parameters is determined for the case of $SU(3)$ and for various other values of the number of colours and several choices of the magnetic flux induced by the twist.