Referenced internal-line decomposition of one-loop string integrand and application to gauge and gravitational beta functions

[2512.23968] Referenced internal-line decomposition of one-loop string integrand and application to gauge and gravitational beta functions Skip to main content Search Submit Donate Log in High Energy Physics - Theory arXiv:2512.23968 (hep-th) [Submitted on 30 Dec 2025 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: Referenced internal-line decomposition of one-loop string integrand and application to gauge and gravitational beta functions Authors: Yao Li View PDF HTML (experimental) Abstract: Following the ideas of Refs.[1,2], we systematically reformulate and generalize the de- composition of one-loop string integrands according to the internal states propagating in a chosen loop channel, extending the construction to both bosonic and heterotic string theories. Using the chiral-splitting formalism, we make manifest a double-copy structure between the left- and right-moving internal loop states. As an application, we analyze the one-loop beta functions of gauge and gravitational couplings from the low-energy field- theory limit of heterotic one-loop three-point amplitudes under a naive $T^6$ compactification. Although maximal supersymmetry forces these beta functions to vanish, our internal-state decomposition provides model-independent expressions for the contributions of different internal loop states. We further show explicitly that both the gravitational beta function and the gravitational correction to the gauge beta function vanish. Comments: 34 pages, 2 figures. The revised version accepted by JHEP Subjects: High Energy Physics - Theory (hep-th) Cite as: arXiv:2512.23968 [hep-th] (or arXiv:2512.23968v3 [hep-th] for this version) https://doi.org/10.48550/arXiv.2512.23968 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yao Li [ view email ] [v1] Tue, 30 Dec 2025 03:43:44 UTC (32 KB) [v2] Sat, 31 Jan 2026 19:45:21 UTC (34 KB) [v3] Thu, 27 Aug 2026 18:49:59 UTC (35 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2025-12 References & Citations INSPIRE HEP NASA ADS 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) Major funding support from

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