Center Vortices and the Gribov Horizon

We show how the infinite color-Coulomb energy of color-charged states is related to enhanced density of near-zero modes of the Faddeev-Popov operator, and calculate this density numerically for both pure Yang-Mills and gauge-Higgs systems at zero temperature, and for pure gauge theory in the deconfined phase. We find that the enhancement of the eigenvalue density is tied to the presence of percolating center vortex configurations, and that this property disappears when center vortices are either removed from the lattice configurations, or cease to percolate. We further demonstrate that thin center vortices have a special geometrical status in gauge-field configuration space: Thin vortices are located at conical or wedge singularities on the Gribov horizon. We show that the Gribov region is itself a convex manifold in lattice configuration space. The Coulomb gauge condition also has a special status; it is shown to be an attractive fixed point of a more general gauge condition, interpolating between the Coulomb and Landau gauges.

[1]  D. Zwanziger.  Equation of state of gluon plasma from a fundamental modular region. , 2004, Physical review letters.

[2]  H. Reinhardt,et al.  Signals of confinement in Green functions of SU(2) Yang-Mills theory. , 2004, Physical Review Letters.

[3]  D. Zwanziger,et al.  Coulomb energy, remnant symmetry, and the phases of non-Abelian gauge theories , 2004, hep-lat/0401003.

[4]  J. Greensite,et al.  Center dominance in SU(2) gauge-Higgs theory , 2003, hep-lat/0310057.

[5]  J. Greensite,et al.  Coulomb Energy, Vortices, and Confinement , 2003, hep-lat/0302018.

[6]  J. Greensite.  The Confinement Problem in Lattice Gauge Theory , 2003, hep-lat/0301023.

[7]  D. Zwanziger.  No confinement without Coulomb confinement. , 2002, Physical review letters.

[8]  K. Langfeld.  Lattice effective theory and the phase transition at finite densities , 2002, hep-lat/0212032.

[9]  R. Janik.  New multicritical random matrix ensembles , 2002, hep-th/0201167.

[10]  P. Forcrand,et al.  t Hooft loops and consistent order parameters for confinement , 2001, hep-lat/0110135.

[11]  K. Langfeld.  Confinement versus color superconductivity: a lattice investigation , 2001, hep-lat/0109033.

[12]  H. Reinhardt,et al.  Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition , 2000 .

[13]  M. Lavelle,et al.  Hadrons without strings , 1999, hep-ph/9910398.

[14]  M. Burkardt.  Gauge field theories on a ⊥ lattice , 1999, hep-th/9908195.

[15]  J. Greensite,et al.  The Structure of projected center vortices in lattice gauge theory , 1999, hep-lat/9903023.

[16]  P. Forcrand,et al.  Relevance of center vortices to QCD , 1999, hep-lat/9901020.

[17]  D. Zwanziger,et al.  Renormalizable non-covariant gauges and Coulomb gauge limit , 1998, hep-th/9807024.

[18]  D. Zwanziger.  Renormalization in the Coulomb gauge and order parameter for confinement in QCD , 1998 .

[19]  J. Verbaarschot,et al.  Microscopic Universality in the Spectrum of the Lattice Dirac Operator , 1997, hep-lat/9704018.

[20]  Heller,et al.  Spatial string tension in the deconfined phase of (3+1)-dimensional SU(2) gauge theory. , 1993, Physical review letters.

[21]  B. Petersson,et al.  SPACELIKE WILSON LOOPS AT FINITE-TEMPERATURE , 1993, hep-lat/9306015.

[22]  J. Kertész.  Existence of weak singularities when going around the liquid-gas critical point , 1989 .

[23]  Manousakis,et al.  Nonperturbative length scale in high-temperature QCD. , 1987, Physical review letters.

[24]  V. A. Franke,et al.  A variational principle for the Lorentz condition and restriction of the domain of path integration in non-abelian gauge theory , 1986 .

[25]  C. Borgs.  Area law for spatial Wilson loops in high-temperature lattice gauge theories , 1985 .

[26]  M. Virasoro,et al.  The phase structure of a non-abelian gauge Higgs field system , 1981 .

[27]  E. Fradkin,et al.  Phase diagrams of lattice gauge theories with Higgs fields , 1979 .

[28]  V. N. Gribov,et al.  Quantization of non-Abelian gauge theories , 1978 .