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Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
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Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
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We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.
Forward citations
Cited by 8 Pith papers
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Exotic theta terms in 2+1d fractonic field theory
Exotic theta terms in 2+1d fractonic φ-theory induce generalized Witten effects, with vortex operators gaining momentum subsystem charge (quadrupolar for the foliated case).
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Lattice chiral symmetry from bosons in 3+1d
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
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Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints
Modulated SPT phases in 1D are classified by H²(G, U(1)_s) and obey LSM-type theorems forbidding symmetric short-range entangled ground states.
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The Line, the Strip and the Duality Defect
Condensation defects in SymTFT descriptions of XY-plaquette and XYZ-cube models realize non-invertible self-duality symmetries at any coupling, with a continuous SO(2) version in the XY-plaquette.
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There and Back Again: A Gauging Nexus between Topological and Fracton Phases
Gauging the 1-form symmetry in the X-Cube construction produces a web of relations to SPT phases with subsystem and higher-form symmetries plus subsystem symmetry fractionalization in the 3+1D toric code.
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Develops a Mille-feuille SymTFT construction that generates foliated and exotic dual bulk theories realizing gapless boundary models with spontaneous continuous subsystem symmetry breaking, including duals of the XY p...
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Fractonic solids
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This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
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