Anomaly Enforced Gaplessness for Background Flux Anomalies and Symmetry Fractionalization

Anomalous symmetries are known to strongly constrain the possible IR behavior along any renormalization group (RG) flow. Recently, the extension of the notion of symmetry in QFT has provided new types of anomalies with a corresponding new class of constraints on RG flows. In this paper, we derive the constraints imposed on RG flows from anomalies that can only be activated in the presence of specific background fluxes even though they do not necessarily correspond to a symmetry. We show that such anomalies can only be matched by gapped theories that exhibit either spontaneous symmetry breaking or symmetry fractionalization. In addition, we exhibit previously unstudied examples of these flux background anomalies that arise in $4d$ QCD and $4d$ SUSY QCD.