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Fracton phases of matter are gapped phases of matter that, by dint of theirsensitivity to UV data, demand non-standard quantum field theories to describethem in the IR. Two such approaches are foliated quantum theory and exoticfield theory. In this paper, we explicitly construct a map from one to theother and work out several examples. In particular, we recover the equivalencebetween the foliated and exotic fractonic BF theories recently demonstrated atthe level of operator correspondence. We also demonstrate the equivalence oftoric code layers and the anisotropic model with lineons and planons to thefoliated BF theory with one and two foliations, respectively. Finally, wederive new exotic field theories that provide simple descriptions of hybridfracton phases from foliated field theries known to do so. Our results bothprovide new examples of exotic field theories and pave the way toward theirsystematic construction from foliated field theories.

Exotic Field Theories for (Hybrid) Fracton Phases from Imposing Constraints in Foliated Field Theory