Chiral symmetry breaking as a consequence of nontrivial spatial topology

TL;DR

This paper demonstrates that a pointlike magnetic vortex in 2+1 dimensions induces chiral symmetry breaking in the vacuum, leading to observable condensates and currents even outside the magnetic flux region.

Contribution

It reveals how a singular magnetic vortex causes vacuum polarization and symmetry breaking, with detailed dependence on flux and boundary conditions, extending understanding of topological effects in quantum field theory.

Findings

Chiral condensate and currents are generated by the vortex.

Vacuum characteristics depend on flux and boundary conditions.

The effect persists outside the magnetic flux region.

Abstract

A singular configuration of external static magnetic field in the form of a pointlike vortex polarizes the vacuum of quantized massless spinor field in 2+1-dimensional space-time. This results in an analogue of the Bohm-Aharonov effect: the chiral symmetry breaking condensate, energy density and current emerge in the vacuum even in the case when the spatial region of nonvanishing external field strength is excluded. The dependence of the vacuum characteristics both on the value of the vortex flux and on the choice of the boundary condition at the location of the vortex is determined.