{
  "abstract": "We study the quantization of an M2 brane wrapping $\\mathrm{AdS}_2\\times S^1$ inside $\\mathrm{AdS}_4\\times S^7/\\mathbb{Z}_k$, dual to the $\\frac{1}{2}$-BPS circular Wilson loop in ABJM theory. The classical action and the one-loop contribution were previously shown to reproduce the gauge-theory localization result. Here we extend the analysis to the two-loop order. In an adapted static and $κ$-symmetry gauge the world-volume action contains no cubic interaction vertices, so that the two-loop correction is determined entirely by quartic interactions and is manifestly free of logarithmic UV divergences. We find that the bosonic and fermionic contributions combine into a perfect square $ {\\mathscr X}^2$ where ${\\mathscr X}$ is a linear combination of the bosonic and fermionic 3d Green's functions and their derivatives. The evaluation of $\\mathscr X$ requires fixing the $\\mathrm{AdS}_2$ boundary quantization of the massless fermionic modes. With the boundary conditions selected by the preserved supersymmetry, $\\mathscr X$ vanishes and hence the complete two-loop correction is found to be zero. This result would not be consistent with identifying the M2-brane loop expansion directly with the large-$N$ expansion of the canonical, fixed-$(N,k)$ localization prediction. Instead, it agrees precisely with the recent proposal that the semiclassical M2-brane partition function should be matched to the gauge-theory grand-canonical ensemble, in which the Wilson loop expectation value is perturbatively one-loop exact. The vanishing of the two-loop correction thus provides a non-trivial test of this grand-canonical identification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14497",
  "author_total": 4,
  "authors": [
    {
      "name": "M. Beccaria"
    },
    {
      "name": "S. A. Kurlyand"
    },
    {
      "name": "A. A. Tseytlin"
    },
    {
      "name": "J. van Muiden"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28vq9hg9hkrt6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14497",
  "fulltext_url": null,
  "id": "28vq9hg9hkrt6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14497",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7213322883",
  "pdf_url": "https://arxiv.org/pdf/2609.14497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28vq9hg9hkrt6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2609.14497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14497"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "M2 brane in AdS$_4\\times S^7/\\mathbb Z_k$: 2-loop correction to $\\frac{1}{2}$-BPS Wilson loop vs localization in ABJM theory",
  "title_text": "M2 brane in AdS_4× S^7/ℤ_k: 2-loop correction to 1/2-BPS Wilson loop vs localization in ABJM theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/28vq9hg9hkrt6",
  "venue": "arXiv",
  "versions": []
}