Stochastic confinement and dimensional reduction

Parity breaking at high temperature and density

“…One could try to discard these lattice results by saying that the lattices are too small, and that we are far from continuum physics. However, from the simulations of pure SU(2) gauge theories in three dimensions it is known [23] that the scaling region is reached already at β G = 5 and that the correlation length at this value is quite small. For the pure gauge theory we can therefore approach continuum physics on quite small lattices.…”

“…The infra-red singularities in three-dimensional non-Abelian gauge theories (and the magnetic sector of high temperature four-dimensional non-Abelian gauge theories) can be cured by a dynamical generated mass scale. We believe such a mass scale is generated for the string tension [23] and the glueball mass [24,25] in the symmetric phase. This mass scale could then counteract the potential instability coming from a ChernSimons term.…”

“…The above reported results are in qualitative agreement with the existence of such a mass scale which would prevent any spontaneous parity breaking. In fact we can, somewhat courageously, use the toy model (23) to estimate the non-perturbative mass m 2 which enters in the action, since we have determined the critical µ-value where the tachyonic mode begins to dominate. The most obvious comparison is made between the lattice version ofÕ cont 3 and (23), since the non-local lattice action is closest to the Chern-Simons like term in (23).…”

“…In fact we can, somewhat courageously, use the toy model (23) to estimate the non-perturbative mass m 2 which enters in the action, since we have determined the critical µ-value where the tachyonic mode begins to dominate. The most obvious comparison is made between the lattice version ofÕ cont 3 and (23), since the non-local lattice action is closest to the Chern-Simons like term in (23). After a little algebra we find that the naive relation between the µ which appears in (23) and µ 3 multiplying the lattice action is given by µ a = 8µ 3 β G…”

Glueballs, strings and topology in SU(N) gauge theory

“…The values of σ k are interesting because they carry information about confinement. Also because there are specific conjectures about their values from M(-theory)QCD [8], from arguments about Casimir scaling [12], and from certain models, such as the bag model [13]. Moreover such strings may have striking implications [6,7] for the glueball mass spectrum as a function of N .…”