Quarks with Twisted Boundary Conditions in the Epsilon Regime

TL;DR

This paper investigates how twisted boundary conditions influence quark behavior in the epsilon regime of chiral perturbation theory, deriving partition functions and condensates, and proposing a method to extract the pion decay constant from simulations.

Contribution

It provides the first detailed analysis of twisted boundary effects on chiral condensates and partition functions in the epsilon regime, including new formulas for non-degenerate and massless/massive quark theories.

Findings

Chiral symmetry remains restored in finite volumes despite twisted boundary conditions.

Dependence of the condensate on twisting parameters enables extraction of the pion decay constant.

Topological charge sector contributions are insensitive to twisting conditions.

Abstract

We study the effects of twisted boundary conditions on the quark fields in the epsilon regime of chiral perturbation theory. We consider the $SU(2)_L\times SU(2)_R$ chiral theory with non-degenerate quarks and the $SU(3)_L\times SU(3)_R$ chiral theory with massless up and down quarks and massive strange quarks. The partition function and condensate are derived for each theory. Because flavor-neutral Goldstone bosons are unaffected by twisted boundary conditions chiral symmetry is still restored in finite volumes. The dependence of the condensate on the twisting parameters can be used to extract the pion decay constant from simulations in the epsilon regime. The relative contribution to the partition function from sectors of different topological charge is numerically insensitive to twisted boundary conditions.