Instantons and Gribov Copies in the Maximally Abelian Gauge

Abstract

We calculate the Faddeev-Popov operator corresponding to the maximally Abelian gauge for gauge group SU(N). Specializing to SU(2) we look for explicit zero modes of this operator. Within an illuminating toy model (Yang-Mills mechanics) the problem can be completely solved and understood. In the field theory case we are able to find an analytic expression for a normalizable zero mode in the background of a single `t Hooft instanton. Accordingly, such an instanton corresponds to a horizon configuration in the maximally Abelian gauge. Possible physical implications are discussed.

31 pages, 8 figures, v3: references added

References in corpus (2)

• Colour confinement and dual superconductivity of the vacuum - I
• Monopole characteristics in various Abelian gauges

Cited by in corpus (26)

• Problems in Lattice Gauge Fixing
• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• A study of the Gribov copies in linear covariant gauges in Euclidean Yang-Mills theories
• Non-Abelian Stokes Theorem and Quark Confinement in SU(N) Yang-Mills Gauge Theory
• The gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: taking into account the effects of the Gribov copies and of the dimension two condensates
• The influence of the Gribov copies on the gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge
• A study of the maximal Abelian gauge in SU(2) Euclidean Yang-Mills theory in the presence of the Gribov horizon
• Study of the properties of the Gribov region in SU(N) Euclidean Yang-Mills theories in the maximal Abelian gauge
• Study of the Gribov region in Euclidean Yang-Mills theories in the maximal Abelian gauge
• Gribov horizon and non-perturbative BRST symmetry in the maximal Abelian gauge
• Non-Abelian Stokes Theorem and Quark Confinement in SU(3) Yang-Mills Gauge Theory
• Magnetic monopoles vs. Hopf defects in the Laplacian (Abelian) gauge
• Gribov-Zwanziger action in SU(2) Maximally Abelian Gauge with U(1)${}_3$ Landau Gauge
• A few remarks on the zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges
• Ghost Condensates and Dynamical Breaking of SL(2,R) in Yang-Mills in the Maximal Abelian Gauge
• Derivation of an Abelian effective model for instanton chains in 3D Yang-Mills theory
• Study of the zero modes of the Faddeev-Popov operator in the maximal Abelian gauge
• A study of the zero modes of the Faddeev-Popov operator in Euclidean Yang-Mills theories in the Landau gauge in d=2,3,4 dimensions
• Effective sigma models and lattice Ward identities
• Yang-Mills theory in the maximal Abelian gauge in presence of scalar matter fields
• Hopf defects as seeds for monopole loops
• Infinitesimal Gribov copies in gauge-fixed topological Yang-Mills theories
• Study of the nonlocal gauge invariant mass operator $\mathrm{Tr}\int d^{4}x{F}_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$ in the maximal Abelian gauge
• Non-perturbative aspects of Yang-Mills theories
• Yang-Mills instanton as a quantum black hole
• Study of the all orders multiplicative renormalizability of a local matter confining Gribov-Zwanziger action in the MAG