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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2025
Main Authors: Mariño, Marcos, Miravitllas, Ramon, Reis, Tomás
Format: Article
Language:English
Published: Інститут математики НАН України 2025
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/214099
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:On the Structure of Trans-Series in Quantum Field Theory. Marcos Mariño, Ramon Miravitllas and Tomás Reis. SIGMA 21 (2025), 065, 33 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
first_indexed 2026-03-15T09:13:08Z
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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.
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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
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AT miravitllasramon onthestructureoftransseriesinquantumfieldtheory
AT reistomas onthestructureoftransseriesinquantumfieldtheory