  We study "vacuum crossing", which occurs when the vacua of a theory are
exchanged as we vary some periodic parameter $\theta$ in a closed loop. We show
that vacuum crossing is a useful non-perturbative tool to study
strongly-coupled quantum field theories, since finding vacuum crossing in a
weakly-coupled regime of the theory can lead to nontrivial consequences in the
strongly-coupled regime. We start by discussing a mechanism where vacuum
crossing occurs due to an anomaly, and then discuss some applications of vacuum
crossing in general. In particular, we argue that vacuum crossing can be used
to check IR dualities and to look for emergent IR symmetries.
