Paper Citation Record · LEDGER

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation

As of 12 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2607.25332.

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2607.25332 v1

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measured 45 of 45 reference resolution

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Outbound references

Observation bf64bdae-f235-4760-a9f0-fdfb89ec1159 · outbound

This paper cites Goddard, J.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Goddard, J

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:28.348223Z

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Observation 21514514-061d-4672-82e8-e7fb255a3c8f · outbound

This paper cites Montonen and D.I.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Montonen and D.I

Reference 2

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Observation 9247520a-5fad-4079-8c8f-ccf383bd614c · outbound

This paper cites Witten and D.I.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Witten and D.I

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:28.579794Z

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Observation c187a594-9e26-4c7e-a0c1-996e2436bf49 · outbound

This paper cites Osborn,Topological Charges for N=4 Supersymmetric Gauge Theories and Monopoles of Spin 1,Phys.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Osborn,Topological Charges for N=4 Supersymmetric Gauge Theories and Monopoles of Spin 1,Phys

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:28.686233Z

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Observation 5a9c9e0d-1e41-4828-98aa-269823c80d86 · outbound

This paper cites Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:28.834796Z

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Observation d2c1665a-d764-47ba-b08f-35265853ee0c · outbound

This paper cites On S-Duality in Abelian Gauge Theory.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation On S-Duality in Abelian Gauge Theory

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:28.959925Z

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Observation 35352e4f-4028-406d-b17b-83b58adc6745 · outbound

This paper cites Self-dual U(1) lattice field theory with a $\theta$-term.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Self-dual U(1) lattice field theory with a $\theta$-term

Reference 7

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Observation f5d5c715-e6d5-42ec-90d1-5779432e8cb7 · outbound

This paper cites Anosova, C.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Anosova, C

Reference 8

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Observation edb8e68c-8603-44c3-8ee1-eecf8601437e · outbound

This paper cites Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:29.254618Z

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Observation 8894f570-4ee6-4fbb-8ca0-f46d811cb71c · outbound

This paper cites Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:29.329220Z

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Observation 802dff50-9e6e-4629-89e4-95f870c1c752 · outbound

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

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation 2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries

Reference 11

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Observation 604ea434-b874-4c97-99c2-bfcd2d463a0d · outbound

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

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation

Reference 12

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Observation 90f23dde-3724-4a11-a80a-50874357446b · outbound

This paper cites Villain,Theory of one-dimensional and two-dimensional magnets with an easy magnetization plane.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Villain,Theory of one-dimensional and two-dimensional magnets with an easy magnetization plane

Reference 13

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Observation 81797076-8d6b-4e75-8b77-fe706188ace5 · outbound

This paper cites DeGrand and D.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation DeGrand and D

Reference 14

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Observation 3e9fa0f3-f2c0-486b-b0fb-14073723e5fb · outbound

This paper cites Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:29.875493Z

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Observation 32abbd57-2375-4419-81b7-156525448ef5 · outbound

This paper cites Equivalence of the modified Villain formulation and the dual Hamiltonian method in the duality of the XY-plaquette model.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Equivalence of the modified Villain formulation and the dual Hamiltonian method in the duality of the XY-plaquette model

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:30.016441Z

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Observation b1eaad65-6383-473a-a365-b47cf1af6eaa · outbound

This paper cites Canonical quantization of lattice Chern-Simons theory.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Canonical quantization of lattice Chern-Simons theory

Reference 17

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Observation 3d2f68a1-5cea-4d83-ab97-b53f1e672a54 · outbound

This paper cites Ikeda,A Lattice U(1) Chern-Simons Theory via Lattice Deligne-Beilinson Cohomology, 2601.15939.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Ikeda,A Lattice U(1) Chern-Simons Theory via Lattice Deligne-Beilinson Cohomology, 2601.15939

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:30.262225Z

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Observation 38933a90-262e-437f-baa1-b707f59720d7 · outbound

This paper cites Solvable Lattice Hamiltonians with Fractional Hall Conductivity.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Solvable Lattice Hamiltonians with Fractional Hall Conductivity

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:30.378021Z

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Observation c34f77ae-85ea-421d-a10a-5ae5e54271f5 · outbound

This paper cites Fractional Hall Conductivity and Spin-c Structure in Solvable Lattice Hamiltonians.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Fractional Hall Conductivity and Spin-c Structure in Solvable Lattice Hamiltonians

Reference 20

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Observation c9a7bfb4-bdad-4968-a8dc-ec80092edecb · outbound

This paper cites Modified Villain formulation of abelian Chern-Simons theory.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Modified Villain formulation of abelian Chern-Simons theory

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:30.513395Z

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Observation e56cc924-b7a6-41d5-8399-32eda8989539 · outbound

This paper cites Lattice Chern-Simons-Maxwell Theory and its Chirality.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Lattice Chern-Simons-Maxwell Theory and its Chirality

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:30.590932Z

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Observation 05235afa-42a2-42af-ab35-53bb048d5b50 · outbound

This paper cites Lattice realization of compact $U(1)$ Chern-Simons theory with exact 1-symmetries.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Lattice realization of compact $U(1)$ Chern-Simons theory with exact 1-symmetries

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:30.732413Z

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Observation f7ac83e3-171a-4ab6-8547-70b6d349a388 · outbound

This paper cites Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory

Reference 24

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Observation 69fd0974-b5c1-4b42-90c2-7f7a3d655a8f · outbound

This paper cites Dijkgraaf and E.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Dijkgraaf and E

Reference 25

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Observation 7287bd44-6412-4ae8-a6e9-92c8d6b25f62 · outbound

This paper cites Classification of abelian spin Chern-Simons theories.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Classification of abelian spin Chern-Simons theories

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:31.137493Z

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Observation 067da89c-1f8d-47e9-8b30-3cce6c355524 · outbound

This paper cites Onoda,’t Hooft Line in 4D U (1) Lattice Gauge Theory and a Microscopic Description of Dyon’s Statistics,PTEP2026(2026) 013B04 [2505.05050].

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Onoda,’t Hooft Line in 4D U (1) Lattice Gauge Theory and a Microscopic Description of Dyon’s Statistics,PTEP2026(2026) 013B04 [2505.05050]

Reference 27

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Observation 051cd3de-9f2f-4bdf-b0a1-70bcfbab0da6 · outbound

This paper cites Lattice chiral symmetry from bosons in 3+1d.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Lattice chiral symmetry from bosons in 3+1d

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:31.420625Z

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Observation abf530b7-a764-44d3-84ff-cd8ac959bc86 · outbound

This paper cites Witten,Dyons of Charge e theta/2 pi,Phys.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Witten,Dyons of Charge e theta/2 pi,Phys

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:31.541154Z

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Observation fe774144-a3fd-4400-bfa3-7266bfa8b95a · outbound

This paper cites Non-Invertible Duality Defects in 3+1 Dimensions.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Non-Invertible Duality Defects in 3+1 Dimensions

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:31.699646Z

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Observation 4618a523-dcc4-44b4-9b86-bb423b3fe7e5 · outbound

This paper cites Kramers-Wannier-like duality defects in (3+1)d gauge theories.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Kramers-Wannier-like duality defects in (3+1)d gauge theories

Reference 31

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Observation ec0478ff-0e0e-4b1b-aab4-544e98b37ffb · outbound

This paper cites Exploring Non-Invertible Symmetries in Free Theories.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Exploring Non-Invertible Symmetries in Free Theories

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:31.975079Z

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Observation fdbc9ef2-6960-4c96-bd8f-3a175e961355 · outbound

This paper cites What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:32.114213Z

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Observation 696f8a22-4b1e-4c5a-8ff2-bc2e87c21476 · outbound

This paper cites Topological Defects on the Lattice I: The Ising model.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Topological Defects on the Lattice I: The Ising model

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:32.235652Z

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Observation bd2a58e1-bb21-4697-ae45-30b5baa11cad · outbound

This paper cites Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:32.408492Z

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Observation 13ee6aff-fab6-4f46-bf00-1eed5ee32cab · outbound

This paper cites Tambara and S.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Tambara and S

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:32.528382Z

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Observation e974c00a-f297-4d98-8f52-46cb002b7933 · outbound

This paper cites Generalized Global Symmetries.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Generalized Global Symmetries

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:32.688507Z

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Observation 2eb92ca2-5bbb-4c51-9209-17c98596bb5b · outbound

This paper cites New Results in Topological Field Theory and Abelian Gauge Theory.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation New Results in Topological Field Theory and Abelian Gauge Theory

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:32.850687Z

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Observation eb06f0d7-818a-44aa-a271-df950497bd35 · outbound

This paper cites Meynet, D.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Meynet, D

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:32.986561Z

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Observation f73fb4ed-578e-46f2-8468-7dad3abe8332 · outbound

This paper cites Bosonization in three spatial dimensions and a 2-form gauge theory.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Bosonization in three spatial dimensions and a 2-form gauge theory

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:33.129631Z

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Observation 9c6f669e-e4c7-4e04-aa62-866e9f1806cf · outbound

This paper cites Symmetry fractionalization and duality defects in Maxwell theory.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Symmetry fractionalization and duality defects in Maxwell theory

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:33.257805Z

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Observation 564f8017-f455-4363-8852-9f8d10810c5a · outbound

This paper cites Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:33.438630Z

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Observation 4bfe61fc-2b59-420a-b60d-3cc1903fb3d8 · outbound

This paper cites Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:33.551505Z

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Observation 8e43467f-2bf0-4723-a3ef-a07dc9e3f68c · outbound

This paper cites an unresolved cited work.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Unresolved cited work

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:33.649703Z

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Observation 66cb34e5-b3df-4df6-9589-bb4cf2217b01 · outbound

This paper cites Higher cup products on hypercubic lattices: application to lattice models of topological phases.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:33.761192Z

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