Color confinement and dual superconductivity of the vacuum. I

Abstract

We study the dual superconductivity of the ground state of SU͑2͒ gauge theory in connection with confinement. We do this measuring on the lattice a disorder parameter describing condensation of monopoles. Confinement appears as a transition to the dual superconductor, independent of the Abelian projection defining monopoles. Some speculation is made on the existence of a more appropriate disorder parameter. A similar study for SU͑3͒ is presented in a companion paper.

Vortices, monopoles and confinement

“…The vortex corresponds to a string-like topological defect and the dual symmetry does not emerge naturally. In this respect, there is a fundamental difference between the vortex and the monopole picture of colour confinement in terms of symmetry: for the monopoles, a topologically conserved current exists, whose zero component is the generator of the dual symmetry, and a picture based on a mechanism, namely the dual Meissner effect [11], emerges as a consequence of the breaking of the dual symmetry [12]. For the vortices the symmetry pattern is not understood.…”

“…Starting from this point of view, in this paper we study the role of vortices across the deconfinement phase transition, using the techniques developed in Refs. [13,14,12] for investigating the condensation of monopoles defined via the abelian projection.…”

“…When applied to a gauge configuration, µ creates a vortex associated to a string closing in the z direction via periodic boundary conditions (PBC). As well as for other systems, both in statistical mechanics [10,15,16] and in quantum field theory [17,13,14,12], such an operator can be constructed without any reference to the dual theory. In Sect.…”

A disorder analysis of the Ising model

“…The approach [10,[4][5][6][7][8][9] relies on symmetry, and is insensitive to the exact choice of the action, or to irrelevant terms, contrary to the explicit transformation to the dual, which is only possible for specific forms of the action (the Villain action in the XY model and in the U(1) model in (3 + 1)d).…”

“…This has already been done for QCD [9], where the natural topological structures in 3d are monopoles. A clear evidence has emerged of dual superconductivity as the mechanism of colour confinement.…”