Title: Circle compactification and 't Hooft anomaly,
Abstract: Anomaly matching constrains low-energy physics of strongly-coupled field
theories, but it is not useful at finite temperature due to contamination from
high-energy states. The known exception is an 't Hooft anomaly involving
one-form symmetries as in pure $SU(N)$ Yang-Mills theory at $\theta=\pi$.
Recent development about large-$N$ volume independence, however, gives us a
circumstantial evidence that 't Hooft anomalies can also remain under circle
compactifications in some theories without one-form symmetries. We develop a
systematic procedure for deriving an 't Hooft anomaly of the
circle-compactified theory starting from the anomaly of the original
uncompactified theory without one-form symmetries, where the twisted boundary
condition for the compactified direction plays a pivotal role. As an
application, we consider $\mathbb{Z}_N$-twisted $\mathbb{C}P^{N-1}$ sigma model
and massless $\mathbb{Z}_N$-QCD, and compute their anomalies explicitly.