Large volume behaviour of Yang-Mills propagators

Abstract

We investigate finite volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. In particular, we demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. This solves an important open problem of previous studies where the infinite volume limit led to an apparent mismatch, especially of the infrared behaviour, between torus extrapolations and the existing infinite volume solutions obtained in 4-dimensional Euclidean space-time. However, the correct infinite volume limit is approached rather slowly. The typical scales necessary to see the onset of the leading infrared behaviour emerging already imply volumes of at least 10 to 15 fm in lengths. To reliably extract the infrared exponents of the infinite volume solutions requires even much larger ones. While the volumes in the Monte-Carlo simulations available at present are far too small to facilitate that, we obtain a good qualitative agreement of our torus solutions with recent lattice data in comparable volumes.Comment: 34 pages, 8 figures; v2: typos corrected, refs. added, version accepted by Annals of Physic

Decontracted double BRST symmetry on the lattice

“…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:…”

“…This certainly deserves further study, especially with regard to its potential to generalize the topological field theory relation between the Gauss-Bonnet and Poincaré-Hopf theorems [25,48,49]. In fact, an extension to Morse theory similar to (85), but corresponding to the introduction of an imaginary Curci-Ferrari mass parameter [i.e., using a real parameter im 2 t in (85)], and its relation to a generalized Gauss-Bonnet theorem reminiscent of (36) were discussed in Ref. [50].…”

Volume behavior of quark condensate, pion mass, and decay constant from Dyson-Schwinger equations

“…For the ghost and gluon DSE the corresponding equations as well as their solutions have been discussed in detail in Refs. [20][21][22]. The corresponding solutions in the infinite volume/continuum limit are given and discussed in Ref.…”

“…For the gluon propagator we use solutions from the ghost and gluon DSEs as obtained in Refs. [22,23]. There the system of DSEs has been solved using a specific truncation scheme for the ghost-gluon vertex and the three-gluon vertex as input.…”

Numerical approach to Coulomb gauge QCD

“…the ghost propagator is divergent and the gluon propagator vanishes at zero momentum. On the other hand, the interpretation of lattice results is still somewhat controversial, since the IR region is sensitive to finite-volume effects and possible lattice artifacts in mapping between the continuum and lattice definition of propagators [2,[27][28][29][30]. One of the original motivations for such studies follows from the observation that for the physical spectrum to consist only of color-singlet states it is necessary that the ghost and gluon propagators are critical (in the sense defined above) [37,38].…”