Evidence for fine tuning of fermionic modes in lattice gluodynamics

Abstract

We consider properties of zero and near-zero fermionic modes in lattice gluodynamics. The modes are known to be sensitive to the topology of the underlying gluonic fields in the quantum vacuum state of the gluodynamics. We find evidence that these modes are fine tuned, that is exhibit sensitivity to both physical (one can say, hadronic) scale and to the ultraviolet cutoff. Namely, the density of the states is in physical units while the localization volume of the modes tends to zero in physical units with the lattice spacing tending to zero. We discuss briefly possible theoretical implications and also include some general, review-type remarks.

arXiv comment7 pages, 7 eps figures, uses JETP Letters style (included); substantial stylistic changes, discussions added, conclusions unchanged. Supplementary materials and computer animations are available at http://lattice.itep.ru/overlap

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• Chiral superfluidity of the quark-gluon plasma
• Preconditioning Maximal Center Gauge with Stout Link Smearing in SU(3)
• P and CP Violation and New Thermalization Scenario in Heavy Ion Collisions
• On topological properties of vacuum defects in lattice Yang-Mills theories
• Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics
• Topological objects in QCD
• Confining string and its widening in HP1 embedding approach
• Embedded monopoles in quark eigenmodes in SU(2) Yang-Mills Theory
• On the Continuum Limit of Topological Charge Density Distribution