Strong coupling expansion of $1\over 2$ BPS Wilson loop in SYM theory and 2-loop Green-Schwarz string in AdS$_5 \times $S$^5$

[2601.08809] Strong coupling expansion of $1\over 2$ BPS Wilson loop in SYM theory and 2-loop Green-Schwarz string in AdS$_5 \times $S$^5$ Skip to main content Search Submit Donate Log in High Energy Physics - Theory arXiv:2601.08809 (hep-th) [Submitted on 13 Jan 2026 ( v1 ), last revised 25 Aug 2026 (this version, v4)] Title: Strong coupling expansion of $1\over 2$ BPS Wilson loop in SYM theory and 2-loop Green-Schwarz string in AdS$_5 \times $S$^5$ Authors: Matteo Beccaria , Stefan A. Kurlyand , Arkady A. Tseytlin View PDF HTML (experimental) Abstract: The exact localization result for the expectation value of the $1\over 2$ BPS circular Wilson loop in ${\cal N}=4$ SYM theory is given in the planar limit by the famous Bessel function expression: $\langle W\rangle = {2N\over \sqrt \lambda } I_1 ( \sqrt \lambda)$. Expanded in large $\lambda$ and expressed in terms of the AdS$_5 \times $S$^5$ string tension $T= {\sqrt \lambda \over 2\pi}$ this gives $\langle W\rangle = {\sqrt T\over 2\pi g_s} e^{2\pi T} (1- {3\over 16 \pi} T^{-1} + ...)$.The exponential is matched by the value of the action of the string with the AdS$_2$ world volume while the prefactor comes from the 1-loop GS string correction. Here we address the question of how the subleading $T^{-1}$ term could be reproduced by the 2-loop correction in the corresponding partition function of the AdS$_5 \times $S$^5$ GS string expanded near the AdS$_2$ minimal surface. We find that the string correction contains a non-zero UV logarithmic divergence implying that comparison with the SYM result requires a particular subtraction prescription. We discuss implications of this conclusion for checking the AdS/CFT duality at strong coupling. Comments: 26 pages. v2: references added; v3,v4: minor corrections Subjects: High Energy Physics - Theory (hep-th) Report number: Imperial-TP-2025-SK-02 Cite as: arXiv:2601.08809 [hep-th] (or arXiv:2601.08809v4 [hep-th] for this version) https://doi.org/10.48550/arXiv.2601.08809 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Arkady Tseytlin [ view email ] [v1] Tue, 13 Jan 2026 18:48:05 UTC (259 KB) [v2] Tue, 27 Jan 2026 09:24:48 UTC (259 KB) [v3] Sun, 8 Mar 2026 20:04:33 UTC (260 KB) [v4] Tue, 25 Aug 2026 10:09:00 UTC (259 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2026-01 References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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