Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility

Abstract

The topological susceptibility of the SU (3) random vortex world-surface ensemble, an effective model of infrared Yang-Mills dynamics, is investigated. The model is implemented by composing vortex world-surfaces of elementary squares on a hypercubic lattice, supplemented by an appropriate specification of vortex color structure on the world-surfaces. Topological charge is generated in this picture by writhe and self-intersection of the vortex world-surfaces. Systematic uncertainties in the evaluation of the topological charge, engendered by the hypercubic construction, are discussed. Results for the topological susceptibility are reported as a function of temperature and compared to corresponding measurements in SU (3) lattice Yang-Mills theory. In the confined phase, the topological susceptibility of the random vortex world-surface ensemble appears quantitatively consistent with Yang-Mills theory. As the temperature is raised into the deconfined regime, the topological susceptibility falls off rapidly, but significantly less so than in SU (3) lattice Yang-Mills theory. Possible causes of this deviation, ranging from artefacts of the hypercubic description to more physical sources, such as the adopted vortex dynamics, are discussed.

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

“…As far as we know, such a relation is not yet derived for SU(3) directly from the Yang-Mills theory, although some models for the SU(3) vortex (vortex-monopole net) [115,226,227] are proposed and studied, while for SU(2) some works give the numerical evidences for the existence of the vortex-monopole chains [80,225].…”

“…For the vortex surfaces for SU(N), N ≥ 3, may branch and the superimposed magnetic fluxes in general also modify the type of vortex flux, i.e., its direction in color space. See e.g., [115]. The (Z N ) vortex condensation theory for quark confinement put forward by 't Hooft [73], Mack [74], Cornwall [75] and by Nielsen, Olesen and Ambjorn [76] ("Copenhagen vacuum") is that the QCD vacuum is presumed to be filled with closed magnetic vortices, which carry magnetic flux in the center of the gauge group, and have the topology of tubes for D = 3 or surfaces for D = 4 of finite thickness.…”

“…Hence, the differential reduction condition can also be expressed in terms of V µ and X µ in the vector form: 113) or in the Lie algebra form: 115) and the number of conditions for…”

Colorful vortex intersections in SU(2) lattice gauge theory and their influences on chiral properties

“…Lattice simulations have shown that center vortices contribute to the topological charge via writhing, vortex intersections [33][34][35][36][37][38][39][40] and their color structure [41][42][43][44]. Vortices lead also to spontaneous χSB [45][46][47][48][49][50][51][52][53][54][55][56].…”

ApproachingSU(2)gauge dynamics with smearedZ(2)vortices

“…The vortex model can be applied to other infrared features of QCD not immediately related to confinement, such as the topological properties of gauge fields. In particular, it was shown how the topological susceptibility present in QCD can be calculated from center vortices [16][17][18][19][20][21][22][23] and vortices are also able to explain chiral symmetry breaking [24][25][26][27][28][29][30][31][32][33][34][35][36]. This way, the vortex model provides a unified picture for the infrared, low energy sector of QCD, explaining both confinement and the chiral and topological features of the strong interaction.…”