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

Abstract

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 $\overline{MS}$ 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.

arXiv comment7 pages, 2 figures, contribution to the 36th International Symposium on Lattice Field Theory, 22-28 July 2018, Michigan State University, East Lansing, USA

References in corpus (7)

• Trivializing maps, the Wilson flow and the HMC algorithm
• The gradient flow coupling in the Schrödinger Functional
• Studying the gradient flow coupling in the Schrödinger functional
• Large $N$ reduction with the Twisted Eguchi-Kawai model
• Non-perturbative determination of the $\Lambda$-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling
• Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models
• (Dimensional) twisted reduction in large N gauge theories