Abstract
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. We construct the corresponding gauged SSPT phase as a foliated two-form gauge theory. Some instances of the gauged SSPT phase are a variant of the X-cube model with the same ground state degeneracy and the same fusion, but different particle statistics.
Highlights
Twisted foliated two-form gauge theory as gauged subsystem-symmetry protected topological (SSPT) phase Many physical systems are protected by global symmetry, and there are invertible phases that are non-trivial only in the presence of global symmetry, known as symmetry protected topological (SPT) phases
The theory can be interpreted as coupling a G gauge theory to the foliated N two-form gauge field Bk, using the one-form symmetry generated by ηk(a)
The theory can be interpreted as coupling a G gauge theory to the foliated N two-form gauge field Bk using the one-form symmetry corresponding to the N center of the extension G
Summary
The objective of a low-energy effective field theory is to describe the low-energy physics of a physical system while ignoring physics that occurs at higher energies, the details of which are viewed as unimportant. A new kind physics exhibited by so-called fracton models [4, 5]1 necessitate a new kind of effective field theory description The excitations in this class of models are classified by their sub-dimensional mobility: planons and lineons are restricted to move along 2D planes and 1D lines, respectively, while fractons are immobile. A gapped D-dimensional fracton model of length L can have up to O(LD−2) [11, 13, 14] robust zeroenergy non-local degrees of freedom This is a phenomenon of UV/IR mixing: the low energy physics depends on some microscopic details such as the total length measured in lattice spacing.
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