Pith Number

pith:MBOAR7PZ

pith:2026:MBOAR7PZ54TNCKMW57OTI2YTTR

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

Shoto Aoki, Toshinari Takemoto, Yoshio Kikukawa

Lattice Maxwell theory with theta term exhibits exact SL(2,Z) duality in the modified Villain formulation.

arxiv:2604.08736 v3 · 2026-04-09 · hep-lat · cond-mat.str-el · hep-th

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Claims

C1strongest claim

As a result, the ultra-local action with a theta term exhibits an exact SL(2,Z)-duality. We further analyze the SL(2,Z)-structure of Wilson and 't Hooft loops, demonstrating that they transform properly up to a nontrivial phase factor arising from the nontrivial self-linking of the loops.

C2weakest assumption

That the non-local transformation procedure added to the S-transformation removes non ultra-locality from the Poisson resummation without introducing inconsistencies or changing the physical content of the duality.

C3one line summary

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.

Cited by

2 papers in Pith

Stringy T-duality on the lattice and the twisted Villain model

Exotic theta terms in 2+1d fractonic field theory

Receipt and verification

First computed	2026-07-02T00:18:28.490770Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

605c08fdf9ef26d12996efdd346b139c6a52e5fc8707ea43f5edb0ebb2fafa23

Aliases

arxiv: 2604.08736 · arxiv_version: 2604.08736v3 · doi: 10.48550/arxiv.2604.08736 · pith_short_12: MBOAR7PZ54TN · pith_short_16: MBOAR7PZ54TNCKMW · pith_short_8: MBOAR7PZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MBOAR7PZ54TNCKMW57OTI2YTTR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 605c08fdf9ef26d12996efdd346b139c6a52e5fc8707ea43f5edb0ebb2fafa23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b83e27c2a5e30ac7b4e03e99258f609a4a9991f1369c5297000a7916a2546934",
    "cross_cats_sorted": [
      "cond-mat.str-el",
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-lat",
    "submitted_at": "2026-04-09T20:00:03Z",
    "title_canon_sha256": "bcf6a36620625ae298dc78c582d87d63f21464ff515a7f0801c9c6d0c7b45d5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.08736",
    "kind": "arxiv",
    "version": 3
  }
}