What's up with IR gluon and ghost propagators in Landau gauge? A puzzling answer from huge lattices

TL;DR

This study uses large lattice simulations in three and four dimensions to investigate the infrared behavior of gluon and ghost propagators in Landau gauge Yang-Mills theories, addressing discrepancies between analytic predictions and numerical results.

Contribution

It provides new lattice data on large volumes that clarify the infrared behavior of propagators, challenging previous assumptions about their suppression or enhancement.

Findings

Ghost propagator less enhanced than predicted analytically

Gluon propagator remains finite at zero momentum

Large lattices reduce discrepancies between theory and simulation

Abstract

Several analytic approaches predict for SU(N_c) Yang-Mills theories in Landau gauge an enhanced ghost propagator G(p^2) and a suppressed gluon propagator D(p^2) at small momenta. This prediction applies to two, three and four space-time dimensions. Moreover, the gluon propagator is predicted to be null at p = 0. Numerical studies by several groups indeed support an enhanced ghost propagator when compared to the tree-level behavior $1/p^2$ and a finite infrared gluon propagator. However, the agreement between analytic and numerical studies is only at the qualitative level in three and in four dimensions. In particular, the infrared exponent of the ghost propagator seems to be smaller than the one predicted analytically and the gluon propagator seems to display a (finite) nonzero value at zero momentum. It has been argued that this discrepancy might go away once simulations are done on much larger lattice sizes than the ones used up to now. Here we present data in three and four space-time dimensions using huge lattices in the scaling region, i.e. up to 320^3 at beta = 3.0 and up to 128^4 at beta = 2.2, corresponding to V \approx (85 fm)^3 and V \approx (27 fm)^4. Simulations have been done on the IBM supercomputer at the University of Sao Paulo