  We show that matching anomalies under large gauge transformations and large
diffeomorphisms can explain the appearance and non-renormalization of couplings
in effective field theory. We focus on thermal effective field theory where we
argue that the appearance of certain unusual Chern-Simons couplings is a
consequence of global anomalies. As an example, we show that a mixed global
anomaly in four dimensions fixes the chiral vortical effect coefficient. This
is an experimentally measurable prediction from a global anomaly. For certain
situations, we propose a simpler method for calculating global anomalies which
uses correlation functions rather than eta invariants.
