The twisted gradient flow coupling at one loop

Understand

We compute the one-loop running of the $SU(N)$ 't Hooft coupling in a finite volume gradient flow scheme using twisted boundary conditions.

• The coupling is defined in terms of the energy density of the gradient flow fields at a scale $\tilde{l}$ given by an adequate combination of the torus size and the rank of the gauge group, and is computed in the continuum using dimensional regularization.
• We present the strategy to regulate the divergences for a generic twist tensor, and determine the matching to the $\overline{\rm MS}$ scheme at one-loop order.
• For the particular case in which the twist tensor is non-trivial in a single plane, we evaluate the matching coefficient numerically and determine the ratio of $\Lambda$ parameters between the two schemes.