Topological order and the vacuum of Yang-Mills theories

Abstract

We study, for $SU(2)$ Yang-Mills theories discretized on a lattice, a non-local topological order parameter, the center flux ${{z}}$. We show that: i) well defined topological sectors classified by $\pi_1(SO(3))=\mathbb{Z}_2$ can only exist in the ordered phase of ${{z}}$; ii) depending on the dimension $2 \leq d\leq 4$ and action chosen, the center flux exhibits a critical behaviour sharing striking features with the Kosterlitz-Thouless type of transitions, although belonging to a novel universality class; iii) such critical behaviour does not depend on the temperature $T$. Yang-Mills theories can thus exist in two different continuum phases, characterized by an either topologically ordered or disordered vacuum; this reminds of a quantum phase transition, albeit controlled by the choice of symmetries and not by a physical parameter.Comment: 32 pages, 15 figures. Typos corrected; to appear on PR

Gribov horizon and Gribov copies effect in lattice Coulomb gauge

“…Alternatively one could argue that, since the fundamental discretization of Yang-Mills theory is known to possess lattice artifacts which affect gauge invariant, topological observables [55][56][57][58], it is conceivable for them to also influence gauge dependent quantities. In this case, it is the discretization of the model itself which would introduce spurious quasi-zero modes in the FP operator which subsequently affect all quantities that require its inversion (such as the ghost propagator or the Coulomb potential).…”

Coulomb versus physical string tension on the lattice

“…A precise relationship between such a gauge-fixed, so called P-vortices and the topological center vortices originally introduced by 't Hooft[52] is still missing. The interested reader is referred to Refs [53][54][55][56][57][58][59][60][61][62][63][64][65]. for further discussions on the subject.…”