On the Structure of Trans-Series in Quantum Field Theory
Many observables in quantum field theory can be expressed as trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or renormalons. Even after Borel resummation of the series in the coupling constant, one has to sum t...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214099 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Structure of Trans-Series in Quantum Field Theory. Marcos Mariño, Ramon Miravitllas and Tomás Reis. SIGMA 21 (2025), 065, 33 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860278252199739392 |
|---|---|
| author | Mariño, Marcos Miravitllas, Ramon Reis, Tomás |
| author_facet | Mariño, Marcos Miravitllas, Ramon Reis, Tomás |
| citation_txt | On the Structure of Trans-Series in Quantum Field Theory. Marcos Mariño, Ramon Miravitllas and Tomás Reis. SIGMA 21 (2025), 065, 33 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Many observables in quantum field theory can be expressed as trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or renormalons. Even after Borel resummation of the series in the coupling constant, one has to sum this infinite series of small exponential corrections. It has been argued that this leads to a new divergence, sometimes called the OPE divergence. We show that, in some interesting examples in quantum field theory, the series of small exponential corrections is convergent, order by order in the coupling constant. In particular, we give numerical evidence for this convergence property in the case of the free energy of integrable asymptotically free theories, which has been intensively studied recently in the framework of resurgence. Our results indicate that, in these examples, the Borel resummed trans-series leads to a well-defined function, and there are no further divergences.
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| first_indexed | 2026-03-15T09:13:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214099 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T09:13:08Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Mariño, Marcos Miravitllas, Ramon Reis, Tomás 2026-02-19T11:14:46Z 2025 On the Structure of Trans-Series in Quantum Field Theory. Marcos Mariño, Ramon Miravitllas and Tomás Reis. SIGMA 21 (2025), 065, 33 pages 1815-0659 2020 Mathematics Subject Classification: 81T40; 40G10; 30E15 arXiv:2302.08363 https://nasplib.isofts.kiev.ua/handle/123456789/214099 https://doi.org/10.3842/SIGMA.2025.065 Many observables in quantum field theory can be expressed as trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or renormalons. Even after Borel resummation of the series in the coupling constant, one has to sum this infinite series of small exponential corrections. It has been argued that this leads to a new divergence, sometimes called the OPE divergence. We show that, in some interesting examples in quantum field theory, the series of small exponential corrections is convergent, order by order in the coupling constant. In particular, we give numerical evidence for this convergence property in the case of the free energy of integrable asymptotically free theories, which has been intensively studied recently in the framework of resurgence. Our results indicate that, in these examples, the Borel resummed trans-series leads to a well-defined function, and there are no further divergences. We would like to thank Zoltan Bajnok, Janos Balog, Ovidiu Costin, Stavros Garoufalidis, Santiago Peris, Marco Serone, and Istvan Vona for useful comments and discussions. The work of M.M. and R.M. has been supported in part by the ERC-SyG project “Recursive and Exact New Quantum Theory” (ReNewQuantum), which received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program, grant agreement No. 810573. The work of T.R. is supported by the ERC-COG grant NP-QFT No. 864583 “Non-perturbative dynamics of quantum fields: from new deconfined phases of matter to quantum black holes”, by the MUR-FARE2020 grant No. R20E8NR3HX “The Emergence of Quantum Gravity from Strong Coupling Dynamics”, and by INFN Iniziativa Specifica GAST and ST&FI. We would also like to thank the SwissMAP Research Station at Les Diablerets for hosting the conference “Resurgence and quantization”, which allowed us to discuss the results of this paper with many colleagues. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Structure of Trans-Series in Quantum Field Theory Article published earlier |
| spellingShingle | On the Structure of Trans-Series in Quantum Field Theory Mariño, Marcos Miravitllas, Ramon Reis, Tomás |
| title | On the Structure of Trans-Series in Quantum Field Theory |
| title_full | On the Structure of Trans-Series in Quantum Field Theory |
| title_fullStr | On the Structure of Trans-Series in Quantum Field Theory |
| title_full_unstemmed | On the Structure of Trans-Series in Quantum Field Theory |
| title_short | On the Structure of Trans-Series in Quantum Field Theory |
| title_sort | on the structure of trans-series in quantum field theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214099 |
| work_keys_str_mv | AT marinomarcos onthestructureoftransseriesinquantumfieldtheory AT miravitllasramon onthestructureoftransseriesinquantumfieldtheory AT reistomas onthestructureoftransseriesinquantumfieldtheory |