Cooling for instantons and the Wrath of Nahm

TL;DR

This paper investigates the semi-classical structure of instantons in lattice QCD using improved cooling techniques and operators, revealing insights into their stability and the non-existence of certain self-dual configurations on the 4-torus.

Contribution

It introduces improved actions and operators that reduce discretization errors to study instantons and topological charge with high precision during cooling.

Findings

Improved operators approach integer topological charges within 10^-4 after cooling.

Configurations with |Q|≈1 and |Q|≈2 support the hypothesis that self-dual |Q|=1 instantons cannot exist on the 4-torus.

Cooling stabilizes instantons and reveals their semi-classical structure.

Abstract

The dynamics of instantons and anti-instantons in lattice QCD can be studied by analysing the action and topological charge of configurations as they approach a self-dual or anti-self-dual state, i.e. a state in which S/S_0=|Q|. We use cooling to reveal the semi-classical structure of the configurations we study. Improved actions which eliminate discretization errors up to and including O(a^4) are used to stabilise instantons as we cool for several thousand sweeps. An analogously improved lattice version of the continuum field-strength tensor is used to construct a topological charge free from O(a^4) discretization errors. Values of the action and topological charge obtained with these improved operators approach mutually-consistent integer values to within a few parts in 10^4 after several hundred cooling sweeps. Analysis of configurations with |Q| \approx 1 and |Q| \approx 2 supports the hypothesis that a self-dual |Q|=1 configuration cannot exist on the 4-torus.