One loop calculation of the renormalised anisotropy for improved anisotropic gluon actions on a lattice

TL;DR

This paper calculates the one-loop renormalisation of anisotropy in improved lattice gluon actions using perturbation theory, providing accurate results for SU(3) gauge theories relevant to current simulations.

Contribution

It introduces a perturbative method to compute the renormalised anisotropy for various improved lattice gluon actions, including new Feynman rules for SU(N).

Findings

One-loop anisotropy correction is accurate to 3% for current simulation parameters.

Feynman rules for SU(N) gauge groups with generic anisotropy are derived.

The method applies to Wilson, Symanzik, and tadpole improved actions.

Abstract

Using the infrared dispersion relation of the on shell gluon, we calculate the renormalisation of the the anisotropy to one loop in perturbation theory for lattice Yang-Mills theories, including the Wilson action and actions with Symanzik and/or tadpole improvement. Using twisted boundary conditions as a gauge invariant infrared regulator, we show for an SU(3) gauge group in D=3+1 dimensions that the one loop anisotropy is accurate to O(3%) for a range of g^2 and chi covering current simulations. In doing so we also present Feynman rules for SU(N) gauge groups with generic anisotropy structure (including `3+1' and `2+2' cases).