Aspects of confinement in QCD from lattice simulations

Abstract

We study confinement in quantum chromodynamics via numerical simulations in the framework of lattice gauge theory. In Landau gauge, the mechanism of confinement is related to the infrared behavior of the ghost and gluon propagators via the Gribov-Zwanziger and Kugo-Ojima scenarios. These scenarios entail a scaling behavior. Functional methods in the continuum allow both for this behavior and for decoupling solutions, while lattice simulations in three and four dimensions yield only the latter. A possible explanation for this mismatch is based on limitations of standard lattice gauge fixing methods. Hence, we investigate a number of alternative gauge fixing algorithms in pure SU(2) gauge theory in two, three and four dimensions. We find that stochastic quantization yields an infrared behavior of the propagators in agreement with the results of standard procedures, even though the Faddeev-Popov operator spectrum indicates some different properties. In the strong-coupling limit, our results challenge the standard picture. In particular, we find in a non-perturbative completion of Landau gauge an enormous effect of the Gribov ambiguity. It entails that no subset of infrared solutions can be excluded yet. Moreover, we study the gluon propagator with free boundary conditions. On large lattices, the results mostly show the standard behavior. We also examine non-periodic gauge transformations. Furthermore, we analyze two topics related to the phase diagram of QCD. First, we explore the sign problem for fermions on the lattice by simulating the three-dimensional Thirring model with a complex Langevin equation. The algorithm succeeds in yielding a 'Silver Blaze' behavior of observables, but it does not reliably describe the onset to a phase with non-zero density. Second, we determine properties of the deconfinement phase transition of pure SU(2) gauge theory in 2+1 dimensions, like the critical temperature, by means of the gluon propagator in Landau gauge.