Monopole Condensation in Gauge Theory Vacuum

Despite decades-long efforts, magnetic monopoles were never found as elementary particles. Monopoles and associated currents were directly measured in experiments and identified as topological quasiparticle excitations in emergent condensed matter systems. These monopoles and the related electric-magnetic symmetry were restricted to classical electrodynamics, with monopoles behaving as classical particles. Here we show that the electric-magnetic symmetry is most fundamental a...

We give an outline of a recent proof that the low-energy effective gauge theory exhibiting quark confinement due to magnetic monopole condensation can be derived from QCD without any specific assumption. We emphasize that the low-energy effective abelian gauge theories obtained here give the dual description of the same physics in the low-energy region. They show that the QCD vacuum is nothing but the dual (type II) superconductor.

We give a theoretical framework for defining and extracting non-Abelian magnetic monopoles in a gauge-invariant way in SU(N) Yang-Mills theory to study quark confinement. Then we give numerical evidences that the non-Abelian magnetic monopole defined in this way gives a dominant contribution to confinement of fundamental quarks in SU(3) Yang-Mills theory, which is in sharp contrast to the SU(2) case in which Abelian magnetic monopoles play the dominant role for quark confinem...

We report on evidence that confinement is related to dual superconductivity of the vacuum in full QCD, as in quenched QCD. The vacuum is a dual superconductor in the confining phase, whilst the U(1) magnetic symmetry is realized a la Wigner in the deconfined phase.

A scaling analysis is made of the order parameter describing monopole condensation at the deconfining transition of N_f=2 QCD around the chiral point. In accordance with scaling properties of the specific heat, studied in a previous paper, scaling is consistent with a first order transition. The status of dual superconductivity of the vacuum as a mechanism of color confinement is reviewed.

New evidence is discussed of monopole condensation in the vacuum of SU(2) and SU(3) gauge theories. Monopoles defined by different abelian projections do condense in the transition to the confined phase and show the same behavior. For SU(2) critical indices are determined by finite size scaling analysis and the results agree with the 3d Ising Model, as expected.

We give a gauge-invariant description of the dual superconductivity for deriving quark confinement and mass gap in Yang-Mills theory.

We present a new perspective on the nature of quark and gluon condensates in quantum chromodynamics. We suggest that the spatial support of QCD condensates is restricted to the interiors of hadrons, since these condensates arise due to the interactions of confined quarks and gluons. An analogy is drawn with order parameters like the Cooper pair condensate and spontaneous magnetization experimentally measured in finite samples in condensed matter physics. Our picture explains ...

I construct an isotropic, gauge invariant monopole condensate in SU(2) QCD. It provides a suitable, gauge-invariant vacuum for the dual-Meissner effect to provide QCD colour confinement without violating the isotropy of real space.

Some aspects are discussed of the mechanism of color confinement in QCD by condensation of magnetic monopoles in the vacuum.