The gradient flow running coupling with twisted boundary conditions

Abstract

We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $⟨E(t)⟩$ 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.

27 pages. LaTeX

References in corpus (6)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• Critical slowing down and error analysis in lattice QCD simulations
• The lattice gradient flow at tree-level and its improvement
• The chirally rotated Schrödinger functional with Wilson fermions and automatic O(a) improvement
• Step scaling and the Yang-Mills gradient flow