’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 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. In particular, there is always a mixed anomaly between T and U(1) baryon symmetry. 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.
Lohitsiri, N., & Sulejmanpasic, T. (2022). Comments on QCD3 and anomalies with fundamental and adjoint matter. Journal of High Energy Physics, 2022(10), Article 81. https://doi.org/10.1007/jhep10%282022%29081