Abstract
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.
Highlights
We begin by reviewing the Quantum Chromodynamics (QCD) phase diagram presented in [9]
The phase diagram is consistent with the large N analysis [25,26,27,28,29] and the constraints from ’t Hooft anomalies [3, 8]
The theory is trivially gapped at generic M. It has a first order phase transition line along the negative real axis of M Nf coming from infinity
Summary
A quantum field theory can form various defects by making its coupling constants spacedependent. These localized degrees of freedom are often protected by anomaly inflow [1], generalized anomalies involving coupling constants [2, 3] or higher Berry phase [4,5,6] An example of such defects is interfaces in 3+1 dimensional SU(N ) Yang-Mills theory with a position-dependent θ -angle that interpolates from θ = 0 to θ = 2π.1. Depending on the fermion mass m, the number of flavors Nf and the number of colors N , the interface can either support a topological quantum field theory, a gapless sigma model or a trivially gapped theory These theories appear in the recent discussions on 2+1 dimensional QCD and dualities of ChernSimons-matter theories [14]. Appendix B studies defects in a 3+1 dimensional real scalar theory defined by making the coefficients of the quadratic and the linear term in the potential space-dependent
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