Anomaly Inflow for Subsystem Symmetries

Burnell, Fiona J.; Devakul, Trithep; Gorantla, Pranay; Lam, Ho Tat; Shao, Shu-Heng

doi:10.48550/arxiv.2110.09529

Cited by 9 publications

(16 citation statements)

References 47 publications

(116 reference statements)

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“…The global symmetry of the modified Villain model (2.14) includes: 14 The continuum limit of this modified Villain lattice model is the 2+1d φ-theory of [34,22] with Lagrangian (1.16). See also [58,19,20,59,60,49,50,61,62] for related discussions.…”

Section: Global Symmetrymentioning

confidence: 99%

Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons

Gorantla,

Lam,

Seiberg

et al. 2022

Preprint

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We study field theories with global dipole symmetries and gauge dipole symmetries. The famous Lifshitz theory is an example of a theory with a global dipole symmetry. We study in detail its 1+1d version with a compact field. When this global symmetry is promoted to a U (1) dipole gauge symmetry, the corresponding gauge field is a tensor gauge field. This theory is known to lead to fractons. In order to resolve various subtleties in the precise meaning of these global or gauge symmetries, we place these 1+1d theories on a lattice and then take the continuum limit. Interestingly, the continuum limit is not unique. Different limits lead to different continuum theories, whose operators, defects, global symmetries, etc. are different. We also consider a lattice gauge theory with a Z N dipole gauge group. Surprisingly, several physical observables, such as the ground state degeneracy and the mobility of defects depend sensitively on the number of sites in the lattice.Our analysis forces us to think carefully about global symmetries that do not act on the standard Hilbert space of the theory, but only on the Hilbert space in the presence of defects. We refer to them as time-like global symmetries and discuss them in detail. These time-like global symmetries allow us to phrase the mobility restrictions of defects (including those of fractons) as a consequence of a global symmetry.

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Section: Global Symmetrymentioning

confidence: 99%

Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons

Gorantla,

Lam,

Seiberg

et al. 2022

Preprint

Self Cite

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“…It is also worth mentioning that several 3D symmetry enriched fractonic phases have recently been constructed using the coupled wire formalism [32,[45][46][47][48]. Similar to the subsystem symmetric HOSPTs we present here, these fracton models have sub-dimensionally mobile excitations, but unlike the HOSPTs, these models have fully dispersive gapless surface modes instead of gapped surfaces and gapless hinge modes.…”

Section: Introductionmentioning

confidence: 72%

Interaction Enabled Fractonic Higher-Order Topological Phases

May-Mann,

You,

Hughes

et al. 2022

Preprint

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In this work, we present a collection of three-dimensional higher-order symmetry protected topological phases (HOSPTs) with gapless hinge modes that exist only in strongly interacting systems subject to subsystem symmetry constraints. We use a coupled wire construction to generate three families of microscopic lattice models: insulators with helical hinge modes, superconductors with chiral Majorana hinge modes, and fractionalized insulators with helical hinge modes that carry fractional charge. In particular, these HOSPTs do not require spatial symmetry protection, but are instead protected by subsystem symmetries, and support "fractonic" quasiparticle excitations that move within only a low-dimensional sub-manifold of the system. We analyze the anomaly structure for the boundary theory and the entanglement Hamiltonian, and show that the side surfaces of these HOSPTs, despite being partially gapped, exhibit symmetry anomalies, and can only be realized as the boundary of three-dimensional HOSPT phases.

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“…One may even try to remove these zero-mode states from the model and the exponential degeneracy of the ground states would be gone. We note that the apparent simplicity of removing the zero mode associated with the subsystem symmetry is almost always the case in the effective field theory description [20,21,22,24,26,25]. In the continuum description, however, removing the zero modes leads to a non-locality and break down of the effective field theory.…”

Section: Discussionmentioning

confidence: 89%

Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries

Katsura,

Nakayama

2022

Preprint

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We construct a purely fermionic system with spontaneously broken supersymmetry that shares the common feature with a fracton phase of matter. Our model is gapless due to the Nambu-Goldstone mechanism. It shows a ground-state degeneracy with the "Area-law" entropy due to fermionic subsystem symmetries. In the strongly coupled limit, it becomes a variant of the Nicolai model, and the groundstate degeneracy shows the "Volume-law" entropy. Gauging the fermionic subsystem symmetry has an t'Hooft anomaly by itself, but the would-be gauged theory may possess a fermionic defect that is immobile in certain spatial directions.

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Anomaly Inflow for Subsystem Symmetries

Cited by 9 publications

References 47 publications

Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons

Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons

Interaction Enabled Fractonic Higher-Order Topological Phases

Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries

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