QCD in a finite box: Numerical test studies in the three Leutwyler-Smilga regimes

TL;DR

This study tests Leutwyler-Smilga predictions on the impact of topological charge in finite-volume QCD-like models across different regimes, confirming some predictions and revealing new insights into the role of the functional determinant.

Contribution

It provides numerical tests of Leutwyler-Smilga predictions in a lattice analogue of the Schwinger model across three regimes, including new findings on the functional determinant and topological sensitivity.

Findings

Confirmed predictions in small and large regimes.

New results on the functional determinant's role.

Insights into topological charge sensitivity in the intermediate regime.

Abstract

The Leutwyler-Smilga prediction regarding the (ir)relevance of the global topological charge for QCD in a finite box is subject to a test. To this end the lattice version of a suitably chosen analogue (massive 2-flavour Schwinger model) is analyzed in the small ($V\Sigma m \ll 1$), intermediate ($V\Sigma m \simeq 1$) and large ($V\Sigma m \gg 1$) Leutwyler-Smilga regimes. The predictions for the small and large regimes are confirmed and illustrated. New results about the role of the functional determinant in all three regimes and about the sensitivity of physical observables on the topological charge in the intermediate regime are presented.