Abstract
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.
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Acknowledgments
We are grateful to Zhu-Xi Luo for referring us to [15] and to Ho Tat Lam for a clarification on the anisotropic model. We thank Andreas Karch and Kevin Slagle for comments on the draft and related conversations. We also thank an anonymous JHEP referee for helpful input, especially for helpful comments about the anisotropic theory and for encouraging us to discuss the periods of the gauge fields in some detail.
This work was supported, in part, by the U.S. Department of Energy under Grant DE-SC0022021 and by a grant from the Simons Foundation (Grant 651440, AK).
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Spieler, R.C. Exotic field theories for (hybrid) fracton phases from imposing constraints in foliated field theory. J. High Energ. Phys. 2023, 178 (2023). https://doi.org/10.1007/JHEP09(2023)178
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DOI: https://doi.org/10.1007/JHEP09(2023)178