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

TL;DR

This paper establishes bounds for the ghost propagator in Yang-Mills theories, analyzing lattice data to determine its behavior in different dimensions, and finds it is not enhanced in 3D and 4D but diverges in 2D.

Contribution

The paper provides rigorous bounds for the ghost propagator using eigenvalues of the Faddeev-Popov matrix and applies these to large-scale lattice simulations across dimensions.

Findings

Ghost propagator not enhanced in 3D and 4D

Ghost propagator diverges in 2D with specific power law

Bounds are derived from eigenvalues of the Faddeev-Popov matrix

Abstract

We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau-gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two dimensional case, on the other hand, we find that G(p) diverges as p^{-2-2 kappa} with kappa \approx 0.15, in agreement with Ref. [1]. We note that our discussion is general, although we make an application only to pure gauge theory in Landau gauge. Most of our simulations have been performed on the IBM supercomputer at the University of Sao Paulo.