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

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arxiv 2505.19412 v3 pith:DZUQGXLX submitted 2025-05-26 hep-th hep-lat

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

Nagare Katayama , Yuya Tanizaki This is my paper
classification hep-th hep-lat
keywords modellatticecardy-rabinovicidualityexactmodifiedthetavillain
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The Cardy-Rabinovici model is a toy model of the lattice $U(1)$ gauge theories to study various oblique confinement states associated with the nonzero $\theta$ angles. We reformulate the $2$d version of this model using the modified Villain lattice formalism, and we establish the exact $\theta$ periodicity for the Witten effect and the strong-weak duality at the finite lattice spacings. We then study the phase structure of this model based on the duality, symmetry and anomaly, and the perturbative renormalization group.

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Cited by 4 Pith papers

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  1. Exotic theta terms in 2+1d fractonic field theory

    hep-th 2026-04 unverdicted novelty 7.0

    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).

  2. Numerical Hints for Dyon Condensation at $\theta=2\pi$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory

    hep-lat 2026-06 unverdicted novelty 6.0

    Lattice computation of Wilson-'t Hooft loops supplies numerical evidence for dyon condensation at theta=2pi in SU(2) Yang-Mills.

  3. Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation

    hep-lat 2026-04 unverdicted novelty 6.0

    The ultra-local modified Villain action for lattice Maxwell theory with theta term has exact SL(2,Z) duality, with Wilson and 't Hooft loops transforming up to a phase from self-linking.

  4. Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation

    hep-lat 2026-04 unverdicted novelty 5.5

    Ultra-local lattice Maxwell theory with a theta term has exact SL(2,Z) duality after a non-local redefinition of the S-transformation, with Wilson and 't Hooft loops transforming up to a self-linking phase.