Instantons and Monopoles

Abstract

This study is part of a research program aimed to investigate the relations between instantons, monopoles, and chiral symmetry breaking. Monopoles are important 3-dimensional topological configurations existing in QCD, which are believed to produce colour confinement. Instantons are 4-dimensional topological configurations and are known to be related to chiral symmetry breaking. To study the relation between monopoles and instantons we generate configurations adding to the vacuum state static monopole-antimonopole pairs of opposite charges by use of a monopole creation operator. We observe that the monopole creation operator only adds long monopole loops to the configurations. We then count the number of fermion zero modes using Overlap fermions as a tool. As a result we find that each monopole-antimonopole pair of magnetic charge one adds one zero mode of chirality $\pm 1$, i.e. one instanton of topological charge $\pm 1$.

arXiv admin note: substantial text overlap with arXiv:1412.2704

References in corpus (25)

• More about exactly massless quarks on the lattice
• The Nf=0 heavy quark potential from short to intermediate distances
• Periodic Instantons with non-trivial Holonomy
• Quark confinement and the bosonic string
• Exact T-duality between Calorons and Taub-NUT spaces
• Topological susceptibility at zero and finite $T$ in SU(3) Yang-Mills theory
• Topological susceptibility in the SU(3) gauge theory
• Colour confinement and dual superconductivity of the vacuum - I
• Numerical techniques for lattice QCD in the $\epsilon$--regime
• Lattice QCD in the epsilon-regime and random matrix theory
• A disorder parameter for dual superconductivity in gauge theories
• Exploring the structure of the quenched QCD vacuum with overlap fermions
• Chiral Condensate in the Deconfined Phase of Quenched Gauge Theories
• Operator improvement for Ginsparg-Wilson fermions
• Monopole clusters in Abelian projected gauge theories
• Dynamics of Monopoles and Flux Tubes in Two-Flavor Dynamical QCD
• Topological susceptibility from the overlap
• String tension and monopoles in $T\ne 0$ SU(2) QCD
• The disorder parameter of dual superconductivity in QCD revisited
• Deconfinement transition and monopoles in $T\ne 0$ $SU(2)$ QCD
• Monopole clusters, Z(2) vortices and confinement in SU(2)
• Hadron spectrum, quark masses and decay constants from light overlap fermions on large lattices
• Properties of the Abelian Projection Fields in $SU(N)$ Lattice Gluodynamics
• Monopoles and hadron spectrum in quenched QCD
• Monopole clusters and critical dynamics in four-dimensional U(1)

Cited by in corpus (12)

• The Myriad Uses of Instantons
• Chiral Symmetry Breaking by Monopole Condensation
• Color confinement, chiral symmetry breaking, and catalytic effect induced by monopole and instanton creations
• Monopole and instanton effects in QCD
• Absence of strong CP violation
• An Effective Model for Glueballs and Dual Superconductivity at Finite Temperature
• Repercussions of the Peccei-Quinn axion on QCD
• QCD monopole and sigma meson coupling
• Monopoles, spectra of overlap fermions, and eta-prime meson in external magnetic fields
• Monopole and instanton effects on connected and disconnected correlations for scalar density
• Chiral Symmetry Breaking by Monopole Condensation
• Violation of non-Abelian Bianchi identity and QCD topology