Confinement of color charge is a puzzling property of Yang-Mills gauge
theories that accounts for the fact that quarks and gluonsâ€”the basic
building blocks of matterâ€”are never found in isolation. The property may
be related to how "ghost-field" correlation functions behave near the
region of gauge-configuration space known as the first Gribov horizon,
which (as a consequence of gauge-fixing) is approached from within as
the system's volume tends to infinity. We study the issue for the lattice
version of the theory by performing Monte Carlo simulations, in which
representative "thermalized" gauge configurations are generated and
used for evaluating the desired correlation functions. In order to gain
better control over the limiting behavior of our computed correlation
functions, we propose to venture away from thermalized configurations,
crossing the boundaries imposed by the Gribov horizon.
The main points of this presentation, i.e. the conceptual understanding of
Monte Carlo sampling and finding ways to cross boundaries, are topics in
which Alan has been an inspirational influence.
Work in collaboration with Attilio Cucchieri.