Comments on QCD$_3$ and anomalies with fundamental and adjoint matter

Abstract

't Hooft anomaly matching is powerful for constraining the low energy phases of gauge theories. In 3d one common anomaly is the parity anomaly in a $T$-symmetric theory where one cannot gauge the global symmetry group without breaking the time-reversal symmetry. We find that a $T$-symmetric $\text{SU}(N)$ gauge theory with either fermionic or bosonic matter in the fundamental representation of the gauge group has a parity anomaly between the flavor group and $T$-symmetry provided that there is also a massless Majorana fermion in the adjoint representation of the gauge group. We then analyze the parity anomaly in this theory, together with the more recent mod 16 time-reversal anomaly, and give some free fermion proposals as candidates for the low energy phases consistent with the anomalies. We make brief comments about the large $N$ limit and the $\T$-broken regimes in the conclusion as well as related anomalies in 4d. }