We study 3+1 dimensional SU(N)SU(N)
Quantum Chromodynamics (QCD) with N_fNf
degenerate quarks that have a spatially varying complex mass. It leads
to a network of interfaces connected by interface junctions. We use
anomaly inflow to constrain these defects. Based on the chiral
Lagrangian and the conjectures on the interfaces, characterized by a
spatially varying \thetaθ-parameter,
we propose a low-energy description of such networks of interfaces.
Interestingly, we observe that the operators in the effective field
theories on the junctions can carry baryon charges, and their spin and
isospin representations coincide with baryons. We also study defects,
characterized by spatially varying coupling constants, in 2+1
dimensional Chern-Simons-matter theories and in a 3+1 dimensional real
scalar theory.
Interface junctions in QCD${}_4$