Abelian monopole and vortex condensation in lattice gauge theories

Abstract

We study Abelian monopole and vortex condensation in lattice pure gauge theories. Condensation is detected by means of a disorder parameter defined in terms of a gauge-invariant effective action introduced using the lattice Schrödinger functional. Dirac monopoles condense in the confined phase of U(1) lattice gauge theory. Abelian monopoles and Abelian vortices condense in the confined phase of SU(2) and SU(3) lattice gauge theories.

Abelian chromomagnetic fields and confinement

“…So that in SU(2) and SU(3) gauge theories one could look at the confining vacuum as a coherent Abelian magnetic condensate. Moreover, we also found [25] that a constant Abelian chromomagnetic field at zero temperature is completely screened in the continuum limit, while at finite temperature [38] it seems that the applied field is restored by increasing the temperature. These results strongly suggest that the confinement dynamics is intimately related to Abelian chromomagnetic gauge configurations.…”

Magnetic Monopoles in the Deconfined Phase of Yang-Mills Theories

“…The magnetic condensate in the confined phase, as well as its disappearance at the deconfining transition, has been extensively investigated on the lattice [3,4,5,6,7,8]. Magnetically charged particles have also been supposed to be relevant to some physical properties of the Quark-Gluon Plasma phase above the transition [9,10,11], such as its very low viscosity and diffusion coefficient and its strongly interacting, liquid-like nature.…”

Magnetic monopoles in the high temperature phase of Yang–Mills theories

“…They enter for instance in the mechanism for color confinement based on dual superconductivity of the vacuum [1][2][3], which relates confinement to the spontaneous breaking of a magnetic symmetry induced by monopole condensation: the magnetic condensate disappears at the deconfining phase transition, as lattice simulations have shown extensively [4][5][6][7][8][9].…”