  We investigate low energy limits of massive gauge theories that feature the
Vainshtein mechanism, focussing on the effects of the UV modes that are
integrated out. It turns out that the Goldstone sectors are significantly
influenced by the effects from such modes relative to the effective field
theories where the irrelevant operators induced by heavy modes are simply cast
aside. The effects of the consistently retained higher order corrections affect
the strong coupling and show that the nature of the UV completion influences
the low energy theory significantly. This casts doubts on the naively estimated
environmental strong coupling scale, and on the effectiveness of the
environmental enhancement of screening. The environmental effects by themselves
might not suffice to cure the bad behavior of the theory beyond the vacuum
cutoff.
