Restoration of Chiral Symmetry from a Boundary

TL;DR

This paper investigates how Dirichlet boundary conditions in lattice QCD affect chiral symmetry breaking, revealing that boundary-induced restoration depends on sigma meson properties and requires large lattices to mitigate.

Contribution

The study demonstrates that boundary effects on chiral symmetry restoration are governed by sigma meson scales, not pions, and highlights the need for large lattices to overcome finite size corrections.

Findings

Chiral symmetry restoration depends on sigma meson wavelength.

Finite size effects follow a power-law correction.

Large lattices are necessary to suppress boundary effects.

Abstract

The imposition of Dirichlet boundary conditions in lattice computations obstructs the formation of a chiral condensate. We use chiral perturbation theory and meson models to address the effect of a Dirichlet boundary on chiral symmetry breaking. While pions are the longest-range modes in QCD, the restoration of chiral symmetry due to a boundary is shown not to depend upon the pion Compton wavelength but rather on that of the sigma meson. Power-law finite size corrections are exposed, and require prohibitively large lattices to overcome. We further speculate on the frustration of the chiral condensate for the case of confinement to the surface of a sphere.