Effect of low-lying fermion modes in the $\epsilon$-regime of QCD

TL;DR

This paper studies how low-lying fermion eigenmodes influence the QCD partition function in the epsilon-regime, confirming theoretical predictions for two flavors and highlighting potential issues with the epsilon-expansion for one flavor.

Contribution

It introduces a method to approximate the fermion determinant using low-lying eigenvalues and compares lattice results with analytical predictions in the epsilon-regime of QCD.

Findings

Agreement with Leutwyler and Smilga's predictions for two flavors

Consistent chiral condensate values for two flavors

Discrepancies in condensate determinations for one flavor

Abstract

We investigate the effects of low-lying fermion eigenmodes on the QCD partition function in the $\epsilon$-regime. The fermion determinant is approximated by a truncated product of low-lying eigenvalues of the overlap-Dirac operator. With two flavors of dynamical quarks, we observe that the lattice results for the lowest eigenvalue distribution, eigenvalue sum rules and partition function reproduce the analytic predictions made by Leutwyler and Smilga, which strongly depend on the topological charge of the background gauge configuration. The value of chiral condensate extracted from these measurements are consistent with each other. For one dynamical quark flavor, on the other hand, we find an apparent disagreement among different determinations of the chiral condensate, which may suggest the failure of the $\epsilon$-expansion in the absence of massless Nambu-Goldstone boson.