Renormalization group improved action on anisotropic lattices

TL;DR

This paper develops an improved lattice gauge action for anisotropic lattices using renormalization group techniques, demonstrating effective parameter tuning for anisotropies between 1 and 4.

Contribution

It extends the renormalization group improved action to anisotropic lattices and determines optimal parameters as functions of anisotropy.

Findings

Improvement program works well on anisotropic lattices.

Parameters from isotropic cases significantly improve anisotropic theories.

Effective for anisotropies in the range 1 to 4.

Abstract

We study a block spin transformation in the SU(3) lattice gauge theory on anisotropic lattices to obtain Iwasaki's renormalization group improved action for anisotropic cases. For the class of actions with plaquette and $1\times2$ rectangular terms, we determine the improvement parameters as functions of the anisotropy $\xi= a_s/a_t$. We find that the program of improvement works well also on anisotropic lattices. From a study of an indicator which estimates the distance to the renormalized trajectory, we show that, for the range of the anisotropy $\xi \approx 1$--4, the coupling parameters previously determined for isotropic lattices improve the theory considerably.