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A Modified Villain Formulation of Fractons and Other Exotic Theories

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arxiv 2103.01257 v4 pith:2GMKRWAO submitted 2021-03-01 cond-mat.str-el hep-th

Pranay Gorantla , Ho Tat Lam , Nathan Seiberg , Shu-Heng Shao This is my paper · ORCID
classification cond-mat.str-elhep-th
keywords theoriescontinuumlatticemodelsapproachexoticformulationfractons
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abstract

We reformulate known exotic theories (including theories of fractons) on a Euclidean spacetime lattice. We write them using the Villain approach and then we modify them to a convenient range of parameters. The new lattice models are closer to the continuum limit than the original lattice versions. In particular, they exhibit many of the recently found properties of the continuum theories including emergent global symmetries and surprising dualities. Also, these new models provide a clear and rigorous formulation to the continuum models and their singularities. In appendices, we use this approach to review well-studied lattice models and their continuum limits. These include the XY-model, the $\mathbb{Z}_N$ clock-model, and various gauge theories in diverse dimensions. This presentation clarifies the relation between the condensed-matter and the high-energy views of these systems. It emphasizes the role of symmetries associated with the topology of field space, duality, and various anomalies.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exactly Solvable 1+1d Chiral Lattice Gauge Theories

    hep-th 2026-01 conditional novelty 7.0 of 10

    Anomaly-free chiral U(1) gauge theories in 1+1 dimensions can be written as quadratic, exactly solvable lattice Hamiltonians, with the 34-50 model as an explicit example.

  2. Bosonization versus the Nielsen-Ninomiya theorem

    hep-th 2026-07 conditional novelty 6.5 of 10

    The 2D modified Villain model's Weyl operators reproduce free Dirac correlations in the continuum, and their no-doubler Dirac kernel is non-local, showing exactly how bosonization evades the Nielsen-Ninomiya theorem.

  3. 2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries

    hep-th 2025-05 conditional novelty 6.0 of 10

    The 2d Cardy-Rabinovici model is constructed on a modified Villain lattice, making rescaled theta periodicity and strong-weak duality exact at finite spacing and giving a symmetry-based phase classification.

  4. U(1)-gauged 2-flavor spin system in 3-D

    hep-lat 2025-02 conditional novelty 6.0 of 10

    A U(1)-gauged two-flavor spin model on a 3D lattice shows a transition that is likely weakly first order, passing near a multi-critical point, based on preliminary Monte Carlo data.

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