Time-Reversal Breaking in QCD$_4$, Walls, and Dualities in 2+1 Dimensions

Understand

We study $SU(N)$ Quantum Chromodynamics (QCD) in 3+1 dimensions with $N_f$ degenerate fundamental quarks with mass $m$ and a $\theta$-parameter.

• For generic $m$ and $\theta$ the theory has a single gapped vacuum.
• However, as $\theta$ is varied through $\theta=\pi$ for large $m$ there is a first order transition.
• For $N_f=1$ the first order transition line ends at a point with a massless $\eta'$ particle (for all $N$) and for $N_f>1$ the first order transition ends at $m=0$, where, depending on the value of $N_f$, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory.