Abstract
We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $\langle E(t)\rangle$ is used to define a running coupling at a scale given by the linear size of the finite volume box. We compute the non-perturbative running of the pure gauge $SU(2)$ coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations. We also comment on the inclusion of matter fields.
Highlights
Asymptotic freedom [1, 2] guarantees that at high energies its value is small
We compute the non-perturbative running of the pure gauge SU(2) coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations
In this paper we propose another alternative based on using twisted boundary conditions for the gauge fields as in the twisted Polyakov loop scheme (TPL) scheme
Summary
The twisted boundary conditions were first introduced by ’t Hooft [28] to characterize confinement. The main observation is that the requirement for physical quantities to be periodic can be accomplished by fields that change by a gauge transformation under translations over a period
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