Gauge Theories on a 2+2 Anisotropic Lattice

TL;DR

This paper explores gauge theories on a 2+2 anisotropic lattice, deriving Feynman rules, analyzing renormalizability, and demonstrating Lorentz invariance restoration at one-loop order.

Contribution

It introduces a framework for gauge theories on a 2+2 anisotropic lattice, including derivation of Feynman rules and analysis of continuum limit recovery.

Findings

Feynman rules for Wilson gauge action derived

Renormalizability of the anisotropic lattice theory confirmed

Lorentz invariance restored at one-loop order

Abstract

The implementation of gauge theories on a four-dimensional anisotropic lattice with two distinct lattice spacings is discussed, with special attention to the case where two axes are finely and two axes are coarsely discretized. Feynman rules for the Wilson gauge action are derived and the renormalizability of the theory and the recovery of the continuum limit are analyzed. The calculation of the gluon propagator and the restoration of Lorentz invariance in on-shell states is presented to one-loop order in lattice perturbation theory for $SU(N_c)$ on both 2+2 and 3+1 lattices.