Constraints on the IR behavior of the gluon propagator in Yang-Mills theories

TL;DR

This paper establishes bounds on the zero-momentum gluon propagator in Yang-Mills theories, enabling a controlled extrapolation of lattice data to infinite volume and revealing a finite, nonzero infrared limit in higher dimensions.

Contribution

It provides rigorous bounds and a method for extrapolating lattice data, demonstrating the infrared behavior of the gluon propagator in SU(2) gauge theories across different dimensions.

Findings

Infrared gluon propagator is finite and nonzero in 3D and 4D.

In 2D, the gluon propagator D(0) equals zero.

Results are consistent with previous studies and theoretical expectations.

Abstract

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case we find D(0) = 0, in agreement with Ref. [1]. We suggest an explanation for these results. We note that our discussion is general, although we only apply our analysis to pure gauge theory in Landau gauge. Simulations have been performed on the IBM supercomputer at the University of Sao Paulo.