Domain walls and vortices in chiral symmetry breaking

We study domain walls and vortices in chiral symmetry breaking in a quantum chromodynamic (QCD)-like theory with N flavors in the chiral limit. If the axial anomaly is absent, there exist stable Abelian axial vortices winding around the spontaneously broken U (1) A symmetry and non-Abelian axial vortices winding around both the U (1) A and non-Abelian SU (N ) chiral symmetries. In the presence of the axial anomaly term, metastable domain walls are present and Abelian axial vortices must be attached by N domain walls, forming domain wall junctions. We show that a domain wall junction decays into N non-Abelian vortices attached by domain walls, implying its metastability. We also show that domain walls decay through quantum tunneling by creating a hole bounded by a closed non-Abelian vortex.