Chiral Symmetry Restoration from a Boundary

Abstract

The boundary of a manifold can alter the phase of a theory in the bulk. We explore the possibility of a boundary-induced phase transition for the chiral symmetry of QCD. In particular, we investigate the consequences of imposing homogeneous Dirichlet boundary conditions on the quark fields. Such boundary conditions are sometimes employed in lattice gauge theory computations, for example, when including external electromagnetic fields, or when computing quark propagators with a reduced temporal extent. Homogeneous Dirichlet boundary conditions force the chiral condensate to vanish at the boundary, and thereby obstruct the spontaneous breaking of chiral symmetry in the bulk. We show the restoration of chiral symmetry due to a boundary is a non-perturbative phenomenon depending upon the mechanism of spontaneous symmetry breaking, and utilize the sigma model to exemplify the issues. Within this model, we find that chiral symmetry is completely restored if the length of the compact direction is less than 2.0 fm. For lengths greater than about 4 fm, an approximately uniform chiral condensate forms centered about the midpoint of the compact direction. While the volume-averaged condensate approaches the infinite volume value as the compact direction becomes very long, the finite-size corrections are shown to be power law rather than exponential.

8 pages, 3 figures, v2 refs added, published version

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• Neutron in a Strong Magnetic Field: Finite Volume Effects
• Dual Fermion Condensates in Curved Space
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• Nonperturbative Casimir Effects in Field Theories: aspects of confinement, dynamical mass generation and chiral symmetry breaking
• Charged particles interaction in both a finite volume and a uniform magnetic field II: topological and analytic properties of a magnetic system
• Effective model for pure Yang-Mills theory on ${\mathbb{T}}^2\times {\mathbb{R}}^2$ with Polyakov loops
• Restoration of Chiral Symmetry from a Boundary