Constraints on the Infrared Behavior of the Gluon Propagator in Yang-Mills Theories

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 Maas. We suggest an explanation for these results. We note that our discussion is general, although we apply our analysis only to pure gauge theory in the Landau gauge. Simulations have been performed on the IBM supercomputer at the University of São Paulo.

Decontracted double BRST symmetry on the lattice

“…The fact that this term is absent, e.g., as explicitly verified for SUð3Þ in (40), reflects the vanishing of the Euler characteristic of SUðNÞ also for odd N, as mentioned above. The even dimension N 2 À 1 of the algebra is irrelevant in this case, because, for the purpose of cohomology, the parameter space of SUðNÞ behaves as a product of odd-dimensional spheres…”

“…Recently, these effects have been analyzed carefully in the Dyson-Schwinger equations [36,37]. These results together with latest lattice data on huge lattices [38][39][40], corresponding to physical lengths of more than 20 fm in each direction, clearly rule out finite-volume effects as the sole origin for the observed discrepancies.…”

“…While early lattice studies of those propagators [32,33] supported the predicted infrared behavior based on their DysonSchwinger equations qualitatively well [34,35], small but significant differences are increasingly being observed nowadays in detailed comparisons and studies of finitevolume effects [36][37][38][39][40]. In particular, as a result of these differences, the Kugo-Ojima confinement criterion of local quantum field theory is now frequently stated to be violated in the infinite-volume limit:…”

Covariant variational approach to Yang-Mills theory

“…We now have two distinct definitions of the effective action: (ii) Linear response: Compute the effective action directly from the variation principle eq. (6) and obtain the 1PI proper n-point functions as derivatives at ϕ = 0.…”

“…Moreover, the Kuga-Ojima criterion [3,4] argues that there should be a direct link between the deep infrared behavior of the gluon and ghost propagator, and the issue of colour confinement. Most investigations initially found an infrared vanishing, scaling type of solution for the gluon propagator, which is, however, at odds with high-precision lattice simulations [5][6][7][8]. It was only later realized that infrared finite so-called decoupling solutions could also be obtained in the functional approach under certain circumstances [1].…”