Vortices, monopoles and confinement

Abstract

We construct the creation operator of a vortex using the methods developed for monopoles. The vacuum expectation value of this operator is interpreted as a disorder parameter describing vortex condensation and is studied numerically on a lattice in SU (2) gauge theory. The result is that vortices behave in the vacuum in a similar way to monopoles. The disorder parameter is different from zero in the confined phase, and vanishes at the deconfining phase transition. We discuss this behaviour in terms of symmetry. Correlation functions of the vortex creation operator at zero temperature are also investigated. A comparison is made with related results by other groups.

Color Confinement and Dual Superconductivity in Full QCD

“…Alternatively the dual ('t Hooft) line L [6] can be used as a disorder parameter (order parameter of the disordered phase) corresponding to the dualZ N symmetry. Our µ is also a good disorder parameter, and in fact it coincides numerically with L [7,8].…”

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].…”

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

“…These Z i thus really are calculated with a modified weight in which the infinite self-energies of the center monopoles introduced explicitly into the configurations are left out (all other center monopoles are of course still completely suppressed; the integration [dQ 0 ] is over the conventional ensemble which respects the Bianchi identity). Of course, the final result for the dual string tension ultimately depends only on the physical partition functions Z I and Z 0 ; all intermediate partition functions cancel out in the product (8). In practice, it is possible to improve the measurement of the individual expectation values (9) further by using a multi-hit procedure.…”