Comparison of |Q| = 1 and |Q| = 2 gauge-field configurations on the lattice four-torus
2004
21 pages
Published in:
- Annals Phys. 311 (2004) 267-287
e-Print:
- hep-lat/0306010 [hep-lat]
Report number:
- ADP-01-51-T483
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Abstract:
It is known that exactly self-dual gauge-field configurations with topological charge |Q|=1 cannot exist on the untwisted continuum 4-torus. We explore the manifestation of this remarkable fact on the lattice 4-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et. al. for SU(2). We identify three distinct signals for the instability of |Q|=1 configurations, and show that these manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for our |Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than local discretization effects. Monte-Carlo generated SU(3) gauge field configurations are cooled to the self-dual limit using an O(a^4)-improved gauge action chosen to have small but positive O(a^6) errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the O(a^4)-improved gauge-field action with an O(a^4)-improved action constructed from the square of an O(a^4)-improved lattice field-strength tensor, thus having different O(a^6) discretization errors. The number of action-density peaks, the instanton size and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of |Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.- 12.38.Gc
- 11.15.Ha
- 11.15.Kc
- Lattice QCD
- Cooling
- Improved operators
- Lattice gauge theory
- gauge field theory: SU(3)
- lattice field theory: action
- charge: topological
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