  Fracton phases of matter are gapped phases of matter that, by dint of their
sensitivity to UV data, demand non-standard quantum field theories to describe
them in the IR. Two such approaches are foliated quantum theory and exotic
field theory. In this paper, we explicitly construct a map from one to the
other and work out several examples. In particular, we recover the equivalence
between the foliated and exotic fractonic BF theories recently demonstrated at
the level of operator correspondence. We also demonstrate the equivalence of
toric code layers and the anisotropic model with lineons and planons to the
foliated BF theory with one and two foliations, respectively. Finally, we
derive new exotic field theories that provide simple descriptions of hybrid
fracton phases from foliated field theries known to do so. Our results both
provide new examples of exotic field theories and pave the way toward their
systematic construction from foliated field theories.
