Description
In the presence of ’t Hooft anomalies, backgrounds for the
symmetries of a quantum field theory can lead to non-conservation of
Noether currents. When there is a net background charge, the partition
function evaluated on closed manifolds will vanish. For anomalous
symmetries, this statement can also be understood as the anomaly theory
giving rise to a non-trivial anomalous phase for the partition function
even for “rigid” transformations which leave all background fields
unchanged. I will explain how to use these ideas to give a new
derivation for the Freed-Witten anomaly-cancellation condition that can
be applied to non-perturbative backgrounds, and discuss some
implications to the study of non-invertible symmetries.
