  In this note, we will characterize constraints on the possible IR phases of a
given QFT by anomalies in the space of coupling constants. We will give
conditions under which a coupling constant anomaly cannot be matched by a
continuous family of symmetry preserving gapped phases, in which case the
theory is either gapless, or exhibits spontaneous symmetry breaking or a phase
transition. We additionally demonstrate examples of theories with coupling
constant anomalies which can be matched by a family of symmetry preserving
gapped phases without a phase transition and comment on the interpretation of
our results for the spontaneous breaking of "$(-1)$-form global symmetries."
