Theta, Time Reversal, and Temperature

Understand

$SU(N)$ gauge theory is time reversal invariant at $\theta=0$ and $\theta=\pi$.

• We show that at $\theta=\pi$ there is a discrete 't Hooft anomaly involving time reversal and the center symmetry.
• This anomaly leads to constraints on the vacua of the theory.
• It follows that at $\theta=\pi$ the vacuum cannot be a trivial non-degenerate gapped state.