  We continue our exploration of exotic, gapless lattice and continuum field
theories with subsystem global symmetries. In an earlier paper, we presented
free lattice models enjoying all the global symmetries (except continuous
translations), dualities, and anomalies of the continuum theories. Here, we
study in detail the relation between the lattice models and the corresponding
continuum theories. We do that by analyzing the spectrum of the theories and
several correlation functions. These lead us to uncover interesting subtleties
in the way the continuum limit can be taken. In particular, in some cases, the
infinite volume limit and the continuum limit do not commute. This signals a
surprising UV/IR mixing, i.e., long distance sensitivity to short distance
details.
