Cautionary remarks on the moduli space metric for multi-dyon simulations

Abstract

We perform a detailed numerical investigation of the approximate moduli space metric proposed by Diakonov and Petrov [arXiv:0704.3181] for a confining model of dyons. Our findings strongly indicate that only for a small number of dyons at sufficiently low density this metric is positive definite - and, therefore, a valid moduli space metric - throughout a considerable part of configuration space. This poses strong limitations on results obtained by an unrestricted integration over collective coordinates in this model. It also indicates that strong correlations between collective coordinates will be essential for the physical content of a dyon model, which could be exhibited by a suitable simulation algorithm.

20 pages, 6 figures

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Cited by in corpus (16)

• Topology and confinement
• Confining Dyon-Anti-Dyon Coulomb Liquid Model I
• Interacting Ensemble of the Instanton-dyons and Deconfinement Phase Transition in the SU(2) Gauge Theory
• Double-winding Wilson loops and monopole confinement mechanisms
• The Myriad Uses of Instantons
• Adjoint fermion zero-modes for SU(N) calorons
• The Vortex Structure of SU(2) Calorons
• Confining dyon gas with finite-volume effects under control
• Dyon structures in the deconfinement phase of lattice gluodynamics: topological clusters, holonomies and Abelian monopoles
• Different faces of confinement
• Confinement, Holonomy and Correlated Instanton-Dyon Ensemble I: SU(2) Yang-Mills Theory
• Deconfinement Phase Transition in the $SU(3)$ Instanton-dyon Ensemble
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics
• Vacuum structure and string tension in Yang-Mills dimeron ensembles
• Partition Function of Interacting Calorons Ensemble