Generalized Hedgehog ansatz and Gribov copies in regions with non trivial topologies

Abstract

In this paper the arising of Gribov copies both in Landau and Coulomb gauges in regions with non-trivial topologies but flat metric, (such as closed tubes S1XD2, or RXT2) will be analyzed. Using a novel generalization of the hedgehog ansatz beyond spherical symmetry, analytic examples of Gribov copies of the vacuum will be constructed. Using such ansatz, we will also construct the elliptic Gribov pendulum. The requirement of absence of Gribov copies of the vacuum satisfying the strong boundary conditions implies geometrical constraints on the shapes and sizes of the regions with non-trivial topologies.

arXiv comment25 pages; Version accepted for publication on Physical Review D. New References included

References in corpus (19)

• Knots and Particles
• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• Constituent Quarks from QCD
• Modeling the Gluon Propagator in Landau Gauge: Lattice Estimates of Pole Masses and Dimension-Two Condensates
• Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge
• No confinement without Coulomb confinement
• The dynamical origin of the refinement of the Gribov-Zwanziger theory
• The Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge
• Landau gauge within the Gribov horizon
• Glueball masses from an infrared moment problem and nonperturbative Landau gauge
• Glueballs, closed fluxtubes and eta(1440)
• One loop gluon form factor and freezing of alpha_s in the Gribov-Zwanziger QCD Lagrangian
• Gribov Problem for Gauge Theories: a Pedagogical Introduction
• Gribov pendulum in the Coulomb gauge on curved spaces
• Gribov ambiguity in asymptotically AdS three-dimensional gravity
• Gravitationally induced zero modes of the Faddeev-Popov operator in the Coulomb gauge for Abelian gauge theories
• A few remarks on the zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges
• Gribov ambiguities in the maximal Abelian gauge

Cited by in corpus (28)

• Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes
• Hedgehog ansatz and its generalization for self-gravitating Skyrmions
• Non-linear superposition law and Skyrme crystals
• Exact multi-soliton solutions in the four dimensional Skyrme model
• Topologically non-trivial configurations in the 4d Einstein--nonlinear $\sigma$-model system
• Exact Kink Solitons in Skyrme Crystals
• Casimir energy in the Gribov-Zwanziger approach to QCD
• SU(N) Multi-Skyrmions at Finite Volume
• Black hole and BTZ-black string in the Einstein-SU(2) Skyrme model
• The (IR-)relevance of the Gribov ambiguity in SU(2) x U(1) gauge theories with fundamental Higgs matter
• Gribov ambiguity and degenerate systems
• Gravitational catalysis of merons in Einstein-Yang-Mills theory
• Cosmological Einstein-Skyrme solutions with non-vanishing topological charge
• Gribov gap equation at finite temperature
• Hairy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear $\sigma$-model system
• On bounds and boundary conditions in the continuum Landau gauge
• Multi-Skyrmions with orientational moduli
• Solitons in a cavity for the Einstein-SU(2) Non-linear Sigma Model and Skyrme model
• The Gribov problem in Noncommutative QED
• Comments on the compatibility of thermodynamic equilibrium conditions with lattice propagators
• Exact solution of the Einstein-Skyrme model in a Kantowski-Sachs spacetime
• Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear $\sigma$-model system: black holes with NUT, black strings and time-dependent solutions
• Gravitating Meron-like topological solitons in massive Yang-Mills theory and the Einstein-Skyrme model
• Dynamics of gravitating hadron matter in Bianchi-IX cosmological model
• Integrability of the Einstein-nonlinear $SU(2)$ $\sigma$-model in a nontrivial topological sector
• On infrared problems of effective Lagrangians of massive spin 2 fields coupled to gauge fields
• The Gribov phenomenon in flat and curved spaces
• Meronic Einstein-Yang-Mills black hole in 5D and gravitational spin from isospin effect