From Foliated to Exotic Field Theories for Gapped Fracton Phases

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 talk, we briefly introduce both types of field theory and outliine the procedure to obtain one from the other. This procedure recovers the equivalence between the foliated and exotic fractonic BF theories recently demonstrated at the level of operator correspondence. It can also be used 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, it can be used to 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.