{
  "abstract": "We revisit the 2-loop computation of the partition function of the GS superstring expanded near the AdS$_2$ surface in AdS$_5\\times S^5$ and AdS$_4\\times {\\rm CP}^3$, dual to $\\frac{1}{2}$ BPS circular Wilson loop in ${\\cal N}=4$ SYM and ABJM theories. In arXiv:2601.08809 it was done in AdS$_5\\times S^5$ using dimensional regularization and a UV pole was found. Since dimensional regularization is problematic for the GS string, here we use a heat-kernel cutoff instead. Then the contribution of the local path integral measure, proportional to $δ(0)$, can no longer be ignored. We show that it cancels the $δ(0)$ terms coming from the quartic interactions in the action, leaving the square of the difference ${\\rm Str}\\,E$ between the regularized numbers of bosonic and fermionic modes. The result is thus UV finite, the pole of arXiv:2601.08809 being an artefact of dimensional regularization. If all fields are regularized with the same smearing kernel, ${\\rm Str}\\,E=0$ and the 2-loop coefficient $f_2$ vanishes, in tension with $f_2=\\frac{3}{32π^2}$ in SYM theory. In the AdS$_4\\times{\\rm CP}^3$ case the same cancellation leaves a finite term proportional to the square of the coincident value of the massless 2d fermion Green's function, giving, ironically, $f_2=\\frac{3}{32π^2}$ instead of $f_2=0$ required by localization. This term is the level-zero (string) part of the result of arXiv:2609.14497 for the AdS$_2\\times S^1$ M2 brane in AdS$_4\\times S^7/\\mathbb Z_k$, where it is cancelled by the higher $S^1$ modes, which also remove a finite mass shift of the massless fermion in conflict with the AdS$_2$ supersymmetry. This suggests that the type II string path integral measure should contain an extra contribution, supplied in the IIA case by the parent M2 brane; in the AdS$_5\\times S^5$ case it is still to be identified and may resolve the remaining 2-loop mismatch with localization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37096",
  "author_total": 1,
  "authors": [
    {
      "name": "Arkady A. Tseytlin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/433e9hmq9c5xj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37096",
  "fulltext_url": null,
  "id": "433e9hmq9c5xj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37096",
  "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": "W7224101736",
  "pdf_url": "https://arxiv.org/pdf/2610.37096",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/433e9hmq9c5xj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.37096",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37096"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "On 2-loop AdS$_2$ superstring partition function in AdS$_5 \\times S^5$ and AdS$_4\\times CP^3$",
  "title_text": "On 2-loop AdS_2 superstring partition function in AdS_5 × S^5 and AdS_4× CP^3",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/433e9hmq9c5xj",
  "venue": "arXiv",
  "versions": []
}