{
  "abstract": "A bstract : We study Abelian S -duality of Maxwell theory on A -type asymptotically locally Euclidean (ALE) spaces. Unlike on closed four-manifolds, the Maxwell path integral on an ALE space is not naturally a scalar partition function. Rather, it decomposes into theta-function blocks labeled by flat U (1) holonomy sectors on the asymptotic lens-space boundary. We interpret these blocks as components of the Hilbert-space boundary state prepared by the ALE path integral. With this interpretation, the apparent failure of ordinary modularity is replaced by vector-valued modular covariance under the action of the modular group. We test this picture explicitly for Eguchi-Hanson space by gluing it to its orientation reversal. The resulting closed four-manifold is diffeomorphic to S ² × S ² , and the natural pairing of the two ALE boundary states reproduces the standard Maxwell partition function on S ² × S ² . We then refine the construction by turning on electric and magnetic 1-form symmetry backgrounds. In their presence, the ALE theta blocks are not ordinary functions, but sections of a line bundle over the Cartan torus associated with the A N −1 root lattice, reflecting the mixed electric-magnetic 1-form anomaly. We also discuss gauging discrete ℤ k subgroups of the 1-form symmetries and show that the vector-valued boundary-state structure remains the natural covariant framework after gauging. In this sense, ALE spaces behave as chiral building blocks for four-dimensional Maxwell theory: individual ALE blocks carry sector-resolved boundary data, while gluing pairs these sectors to produce an ordinary closed-manifold partition function, much like the pairing of left- and right-moving conformal blocks in two-dimensional CFT.",
  "abstract_shown": true,
  "affiliations": [
    "Durham University"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Mohamed M. Anber",
      "orcid": "0000-0003-2620-5218"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/07hrrygp3n8g8.bib",
  "cited_by": 0,
  "doi": "10.1007/jhep10(2026)183",
  "fulltext_url": null,
  "id": "07hrrygp3n8g8",
  "issns": [
    "1029-8479"
  ],
  "landing_url": "https://link.springer.com/article/10.1007/JHEP10(2026)183",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7162536777",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/JHEP10(2026)183.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": "Springer Science and Business Media LLC",
  "ris": "https://research.draconitic.com/paper/07hrrygp3n8g8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "10.1007/jhep10(2026)183",
      "source": "crossref",
      "url": "https://link.springer.com/article/10.1007/JHEP10(2026)183"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Black Holes and Theoretical Physics",
      "subfield": "high-energy"
    }
  ],
  "title": "S-duality, boundary states, and higher-form symmetries on ALE spaces",
  "title_text": "S-duality, boundary states, and higher-form symmetries on ALE spaces",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/07hrrygp3n8g8",
  "venue": "Journal of High Energy Physics",
  "versions": []
}