Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions
We analyze the asymptotically free massless scalar ³ quantum field theory in 6 dimensions, using resurgent asymptotic analysis to find the trans-series solutions which yield the non-perturbative completion of the divergent perturbative solutions to the Kreimer-Connes Hopf-algebraic Dyson-Schwinger e...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211440 |
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| Cite this: | Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions. Michael Borinsky, Gerald V. Dunne and Max Meynig. SIGMA 17 (2021), 087, 26 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862717034742153216 |
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| author | Borinsky, Michael Dunne, Gerald V. Meynig, Max |
| author_facet | Borinsky, Michael Dunne, Gerald V. Meynig, Max |
| citation_txt | Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions. Michael Borinsky, Gerald V. Dunne and Max Meynig. SIGMA 17 (2021), 087, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We analyze the asymptotically free massless scalar ³ quantum field theory in 6 dimensions, using resurgent asymptotic analysis to find the trans-series solutions which yield the non-perturbative completion of the divergent perturbative solutions to the Kreimer-Connes Hopf-algebraic Dyson-Schwinger equations for the anomalous dimension. This scalar conformal field theory is asymptotically free and has a real Lipatov instanton. In the Hopf-algebraic approach, we find a trans-series having an intricate Borel singularity structure, with three distinct but resonant non-perturbative terms, each repeated in an infinite series. These expansions are in terms of the renormalized coupling. The resonant structure leads to powers of logarithmic terms at higher levels of the trans-series, analogous to logarithmic terms arising from interactions between instantons and anti-instantons, but arising from a purely perturbative formalism rather than from a semi-classical analysis.
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| first_indexed | 2026-03-20T15:48:17Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211440 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-20T15:48:17Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
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| spelling | Borinsky, Michael Dunne, Gerald V. Meynig, Max 2026-01-02T08:34:15Z 2021 Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions. Michael Borinsky, Gerald V. Dunne and Max Meynig. SIGMA 17 (2021), 087, 26 pages 1815-0659 2020 Mathematics Subject Classification: 81T15; 81Q15; 34E10 arXiv:2104.00593 https://nasplib.isofts.kiev.ua/handle/123456789/211440 https://doi.org/10.3842/SIGMA.2021.087 We analyze the asymptotically free massless scalar ³ quantum field theory in 6 dimensions, using resurgent asymptotic analysis to find the trans-series solutions which yield the non-perturbative completion of the divergent perturbative solutions to the Kreimer-Connes Hopf-algebraic Dyson-Schwinger equations for the anomalous dimension. This scalar conformal field theory is asymptotically free and has a real Lipatov instanton. In the Hopf-algebraic approach, we find a trans-series having an intricate Borel singularity structure, with three distinct but resonant non-perturbative terms, each repeated in an infinite series. These expansions are in terms of the renormalized coupling. The resonant structure leads to powers of logarithmic terms at higher levels of the trans-series, analogous to logarithmic terms arising from interactions between instantons and anti-instantons, but arising from a purely perturbative formalism rather than from a semi-classical analysis. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Officeof High Energy Physics under Award Number DE-SC0010339 (GD, MM) and by the NWO Vidi grant 680-47-551 “Decoding Singularities of Feynman graphs” (MB). This work was begun during visits by the first two authors to Humboldt University in 2018 and 2019, and at the Les Houches Summer School in 2018, and we thank these institutions for their hospitality. We are grateful to Marc Bellon, David Broadhurst, Ovidiu Costin, John Gracey, Dirk Kreimer, Enrico Russo, and Karen Yeats for discussions. We also want to thank David Broadhurst for helping with the estimation of the constant in equation (5.26) and for pointing out some typos in a previous version. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions Article published earlier |
| spellingShingle | Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions Borinsky, Michael Dunne, Gerald V. Meynig, Max |
| title | Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions |
| title_full | Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions |
| title_fullStr | Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions |
| title_full_unstemmed | Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions |
| title_short | Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ³ QFT in 6 Dimensions |
| title_sort | semiclassical trans-series from the perturbative hopf-algebraic dyson-schwinger equations: ³ qft in 6 dimensions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211440 |
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