Center vortex model for the infrared sector of Yang–Mills theory — topological susceptibility

Abstract

A definition of the Pontryagin index for SU (2) center vortex world-surfaces composed of plaquettes on a hypercubic lattice is constructed. It is used to evaluate the topological susceptibility in a previously defined random surface model for vortices, the parameters of which have been fixed such as to reproduce the confinement properties of SU (2) Yang-Mills theory. A prediction for the topological susceptibility is obtained which is compatible with measurements of this quantity in lattice Yang-Mills theory.

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].…”

“…Vortices lead also to spontaneous χSB [45][46][47][48][49][50][51][52][53][54][55][56]. As Engelhardt and Reinhardt [33,45] have indicated in SU(2) gauge theory in addition to the location of the vortex surfaces, one needs their orientation to determine contributions of vortices to the topological charge. This relates to the common vortex identification method on the lattice, resulting in P-vortices [7], thin connected surfaces consisting of plaquettes projected to center elements.…”

Center vortex model for the infrared sector ofSU(3)Yang-Mills theory: Vortex free energy

“…This model was first defined and studied for the gauge group SU (2) in refs. [11,35] and later extended to the SU (3) case in refs. [12,36].…”

Confinement and center vortex dynamics in different gauge groups

“…The random vortex world-surface model was initially investigated for SU (2) Yang-Mills theory [8][9][10], and in this simplest case, the main characteristics of the strongly interacting vacuum were reproduced. Both a confining low-temperature phase as well as a deconfined high-temperature phase are found [8], separated by a second-order deconfinement phase transition; furthermore, the topological susceptibility [9,[11][12][13] and the (quenched) chiral condensate [10] match the ones extracted from SU (2) lattice Yang-Mills theory quantitatively.…”

“…The random vortex world-surface model was initially investigated for SU (2) Yang-Mills theory [8][9][10], and in this simplest case, the main characteristics of the strongly interacting vacuum were reproduced. Both a confining low-temperature phase as well as a deconfined high-temperature phase are found [8], separated by a second-order deconfinement phase transition; furthermore, the topological susceptibility [9,[11][12][13] and the (quenched) chiral condensate [10] match the ones extracted from SU (2) lattice Yang-Mills theory quantitatively. Extending the investigation to the SU (3) gauge group [14][15][16], the deconfinement phase transition exhibits weakly first-order behavior [14], and a Y-law for the baryonic static potential is found [15], again matching the corresponding characteristics of SU (3) lattice Yang-Mills theory.…”