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Then

M. Pretko, “Subdimensional particle structure of higher rank U(1) spin liquids,” Phys. Rev. B
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2017
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H. Ma, E. Lake, X. Chen, and M. Hermele, “Fracton topological order via coupled layers,” Phys. Rev. B
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2017
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F. Benini, P.-S. Hsin, and N. Seiberg, “Comments on global symmetries, anomalies, and duality in (2 + 1)d,” JHEP
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2017
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W. Shirley, K. Slagle, Z. Wang, and X. Chen, “Fracton Models on General Three-Dimensional Manifolds,” Physical Review X
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2018
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Y. You, T. Devakul, F. J. Burnell, and S. L. Sondhi, “Subsystem symmetry protected topological order,” Phys. Rev. B

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2021

Comments on Foliated Gauge Theories and Dualities in 3+1d

Hsin, Po-Shen, Slagle, Kevin

Understand

We investigate the properties of foliated gauge fields and construct several foliated field theories in 3+1d that describe foliated fracton orders both with and without matter, including the recent hybrid fracton models.

These field theories describe Abelian or non-Abelian gauge theories coupled to foliated gauge fields, and they fall into two classes of models that we call the electric models and the magnetic models.
We show that these two classes of foliated field theories enjoy a duality.
We also construct a model (using foliated gauge fields and an exactly solvable lattice Hamiltonian model) for a subsystem-symmetry protected topological (SSPT) phase, which is analogous to a one-form symmetry protected topological phase, with the subsystem symmetry acting on codimension-two subregions.