Relevance of Center Vortices to QCD

Abstract

In a numerical experiment, we remove center vortices from an ensemble of lattice SU (2) gauge configurations. This removal adds short-range disorder. Nevertheless, we observe long-range order in the modified ensemble: confinement is lost and chiral symmetry is restored (together with trivial topology), proving that center vortices are responsible for both phenomena. As for the Abelian monopoles, they survive but their percolation properties are lost.

Center vortices and the Gribov horizon

“…4 It seems safe to conclude that this behavior of the F-P observables, found in the Higgs phase, is consistent with an infrared finite Coulomb self-energy. …”

“…We recall that in Coulomb gauge, the hamiltonian is a sum H = H glue + H coul , where Then the excitation energy of the charged state, in SU(N ) gauge theory, is 4) where the {L a } are color group generators, d r the dimension, and C r the quadratic Casimir of representation r of the color charge. Therefore, the excitation energy E r is the energy of the longitudinal color electric field due to the static source, which we can identify as the color Coulomb self-energy.…”

“…The F-P eigenvalue density is an observable which we are able to calculate numerically (section 2), via lattice Monte Carlo and sparse-matrix techniques. Applying standard methods [4] we are able to separate any thermalized lattice configuration into vortex-only and vortex-removed components, and we find that the enhancement of the F-P eigenvalue density can be entirely attributed to the vortex component of the gauge fields. Vortices are associated with an enhancement in the density of F-P eigenvalues λ near λ = 0; this enhancement is key to the divergence of the color-Coulomb energy in Coulomb gauge.…”

Abelian monopole and vortex condensation in lattice gauge theories

“…On the other hand numerical evidence has emerged [14][15][16][17][18][19][20][21][22][23][24][25][26][27] in favor of the so called center vortex picture where the vacuum consists of a coherent condensate of magnetic flux tubes. Also this theoretical proposal has been advanced long time ago [28][29][30][31][32][33][34][35].…”

Role of center vortices in chiral symmetry breaking in SU(3) gauge theory

“…It took until the late '90s until a successful definition was given [16] and the relevance of vortices in the continuum limit was established [17]. The recovery of the string tension from ''vortex-only'' SU(2) gauge configurations (i.e., Z 2 projected from SU(2)) was shown [11][12][13], the finite-temperature deconfinement transition was understood in terms of vortex properties [18][19][20][21] and a connection to D SB was discovered [22][23][24][25].…”