On the spectrum of the Faddeev-Popov operator in topological background fields

Abstract

In the Gribov-Zwanziger scenario the confinement of gluons is attributed to an enhancement of the spectrum of the Faddeev-Popov operator near eigenvalue zero. This has been observed in functional and also in lattice calculations. The linear rise of the quark-anti-quark potential and thus quark confinement on the other hand seems to be connected to topological excitations. To investigate whether a connection exists between both aspects of confinement, the spectrum of the Faddeev-Popov operator in two topological background fields is determined analytically in SU(2) Yang-Mills theory. It is found that a single instanton, which is likely irrelevant to quark confinement, also sustains only few additional zero-modes. A center vortex, which is likely important to quark confinement, is found to contribute much more zero-modes, provided the vortex is of sufficient flux. Furthermore, the corresponding eigenstates in the vortex case satisfy one necessary condition for the confinement of quarks.

arXiv comment14 pages, 4 figures, submitted to EPJC

References in corpus (53)

• Instantons in QCD
• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• The Confinement Problem in Lattice Gauge Theory
• The Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD
• Periodic Instantons with non-trivial Holonomy
• A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge
• Center Dominance and Z2 Vortices in SU(2) Lattice Gauge Theory
• Non-perturbative Landau gauge and infrared critical exponents in QCD
• Infrared behaviour and fixed points in Landau gauge QCD
• On the relevance of center vortices to QCD
• Monopole Constituents inside SU(n) Calorons
• Variational solution of the Yang-Mills Schrödinger equation in Coulomb gauge
• Non-perturbative Faddeev-Popov formula and infrared limit of QCD
• Infrared Exponents and Running Coupling of SU(N) Yang-Mills Theories
• Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory
• Unquenched Gluon Propagator in Landau Gauge
• The Elusiveness of Infrared Critical Exponents in Landau Gauge Yang--Mills Theories
• Towards the infrared limit in SU(3) Landau gauge lattice gluodynamics
• On the Yang-Mills wave functional in Coulomb gauge
• Coulomb Energy, Remnant Symmetry, and the Phases of Non-Abelian Gauge Theories
• Exceptional Deconfinement in G(2) Gauge Theory
• Numerical Study of the Ghost-Gluon Vertex in Landau gauge
• Infrared behaviour of the ghost-gluon vertex in Landau gauge Yang-Mills theory
• Exceptional Confinement in G(2) Gauge Theory
• SU(2) Landau gluon propagator on a 140^3 lattice
• Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory
• Topology of Center Vortices
• Time-independant stochastic quantization, DS equations, and infrared critical exponents in QCD
• High-Temperature Limit of Landau-Gauge Yang-Mills Theory
• Center vortices and Dirac eigenmodes in SU(2) lattice gauge theory
• Center Vortices and the Gribov Horizon
• Signals of confinement in Green functions of SU(2) Yang-Mills theory
• Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory
• Spectral properties of the Landau gauge Faddeev-Popov operator in lattice gluodynamics
• First Evidence for Center Dominance in SU(3) Lattice Gauge Theory
• Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum
• The Universal Renormalization Factors Z_1/Z_3 and Color Confinement Condition in Non-Abelian Gauge Theory
• On the spectrum of the Faddeev-Popov operator in topological background fields
• Infrared Gluon Propagator from lattice QCD: results from large asymmetric lattices
• Center-Vortex Solutions of the Yang-Mills Effective Action in Three and Four Dimensions
• Probing for Instanton Quarks with epsilon-Cooling
• Searching for KvBLL calorons in SU(3) lattice gauge field ensembles
• Center vortex properties in the Laplace center gauge of SU(2) Yang-Mills theory
• Continuum Limits and Exact Finite-Size-Scaling Functions for One-Dimensional $O(N)$-Invariant Spin Models
• Confinement from Instantons or Merons
• Constituents of Doubly Periodic Instantons
• Doubly Periodic Instantons and their Constituents
• Potential energy of Yang-Mills vortices in three and four dimensions
• Vortex induced confinement and the IR properties of Green functions
• Gribov ambiguities and the fundamental domain
• The Infrared Landau Gauge Gluon Propagator from Lattice QCD
• Center vortices in MCG - finite-size and gauge-copy effects
• The Kugo-Ojima Confinement Criterion from Dyson-Schwinger Equations

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