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Resurgence in Deformed Integrable Models / LUCAS SCHEPERS
Swansea University Author: LUCAS SCHEPERS
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Copyright: The Author, Lucas Schepers, 2023. Distributed under the terms of a Creative Commons Attribution 4.0 License (CC BY 4.0).
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DOI (Published version): 10.23889/SUthesis.63254
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Resurgence has been shown to be a powerful and even necessary technique to understand many physical system. The study of perturbative methods in general quantum field theories is hard, but progress is often possible in reduced settings, such as integrable models. In this thesis, we study resurgent e...
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Swansea, Wales, UK
2023
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Institution: | Swansea University |
Degree level: | Doctoral |
Degree name: | Ph.D |
Supervisor: | Thompson, Daniel C. and Nunez, Carlos. |
URI: | https://cronfa.swan.ac.uk/Record/cronfa63254 |
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Distributed under the terms of a Creative Commons Attribution 4.0 License (CC BY 4.0).</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>https://creativecommons.org/licenses/by/4.0/</licence></document></documents><OutputDurs/></rfc1807> |
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v2 63254 2023-04-26 Resurgence in Deformed Integrable Models c486fffc20b25838678b537dd15ed78c LUCAS SCHEPERS LUCAS SCHEPERS true false 2023-04-26 Resurgence has been shown to be a powerful and even necessary technique to understand many physical system. The study of perturbative methods in general quantum field theories is hard, but progress is often possible in reduced settings, such as integrable models. In this thesis, we study resurgent effects in integrable deformations of two-dimensional σ-models in two settings.First, we study the integrable bi-Yang-Baxter deformation of the SU(2) principal chiral model (PCM) and find finite action uniton and complex uniton solutions. Under an adiabatic compactification on an S1, we obtain a quantum mechanical system with an elliptic Lam´e-like potential. We perform a perturbative calculation of the ground state energy of this quantum mechanical system to large orders obtaining an asymptotic series. Using the Borel-Pad´e technique, we determine that the locations of branch cuts in the Borel plane match the values of the uniton and complex uniton actions. Therefore, we can match the non-perturbative contributions to the energy with the uniton solutionswhich fractionate upon adiabatic compactification. An off-shoot of the WKB analysis, is to identify the quadratic differential of this deformed PCM with that of an N = 2 Seiberg-Witten theory. This can be done either as an Nf = 4 SU(2) theory or as an elliptic SU(2) × SU(2) quiver theory. The mass parameters of the gauge theory are given in terms of the bi-Yang-Baxter deformation parameters.Second, we perform a perturbative expansion of the thermodynamic Bethe ansatz (TBA) equations of the SU(N) λ-model with WZW level k in the presence of a chemical potential. This is done with its exact S-matrix and the recently developed techniques [1, 2] using a Wiener-Hopf decomposition, which involve a careful matching of bulk and edge ans¨atze. We determine the asymptotic expansion of this series and compute its renormalon ambiguities in the Borel plane. The analysis is supplemented by a parallel solution of the TBA equations that results in a transseries. The transseries comes with an ambiguity that is shown to precisely match the Borel ambiguity. It is shown that the leading IR renormalon vanishes when k is a divisor of N. E-Thesis Swansea, Wales, UK Integrable Models, Resurgence, Deformations 23 3 2023 2023-03-23 10.23889/SUthesis.63254 COLLEGE NANME COLLEGE CODE Swansea University Thompson, Daniel C. and Nunez, Carlos. Doctoral Ph.D The Royal Society (RGF\R1\180087) 2023-09-28T15:08:55.5379637 2023-04-26T12:36:43.9104550 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics LUCAS SCHEPERS 1 63254__27215__0798ad80f5504d13a8d93b346f60a321.pdf 2023_Schepers_L.final.63254.pdf 2023-04-26T13:12:36.5575955 Output 7888469 application/pdf E-Thesis – open access true Copyright: The Author, Lucas Schepers, 2023. Distributed under the terms of a Creative Commons Attribution 4.0 License (CC BY 4.0). true eng https://creativecommons.org/licenses/by/4.0/ |
title |
Resurgence in Deformed Integrable Models |
spellingShingle |
Resurgence in Deformed Integrable Models LUCAS SCHEPERS |
title_short |
Resurgence in Deformed Integrable Models |
title_full |
Resurgence in Deformed Integrable Models |
title_fullStr |
Resurgence in Deformed Integrable Models |
title_full_unstemmed |
Resurgence in Deformed Integrable Models |
title_sort |
Resurgence in Deformed Integrable Models |
author_id_str_mv |
c486fffc20b25838678b537dd15ed78c |
author_id_fullname_str_mv |
c486fffc20b25838678b537dd15ed78c_***_LUCAS SCHEPERS |
author |
LUCAS SCHEPERS |
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LUCAS SCHEPERS |
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E-Thesis |
publishDate |
2023 |
institution |
Swansea University |
doi_str_mv |
10.23889/SUthesis.63254 |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics |
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description |
Resurgence has been shown to be a powerful and even necessary technique to understand many physical system. The study of perturbative methods in general quantum field theories is hard, but progress is often possible in reduced settings, such as integrable models. In this thesis, we study resurgent effects in integrable deformations of two-dimensional σ-models in two settings.First, we study the integrable bi-Yang-Baxter deformation of the SU(2) principal chiral model (PCM) and find finite action uniton and complex uniton solutions. Under an adiabatic compactification on an S1, we obtain a quantum mechanical system with an elliptic Lam´e-like potential. We perform a perturbative calculation of the ground state energy of this quantum mechanical system to large orders obtaining an asymptotic series. Using the Borel-Pad´e technique, we determine that the locations of branch cuts in the Borel plane match the values of the uniton and complex uniton actions. Therefore, we can match the non-perturbative contributions to the energy with the uniton solutionswhich fractionate upon adiabatic compactification. An off-shoot of the WKB analysis, is to identify the quadratic differential of this deformed PCM with that of an N = 2 Seiberg-Witten theory. This can be done either as an Nf = 4 SU(2) theory or as an elliptic SU(2) × SU(2) quiver theory. The mass parameters of the gauge theory are given in terms of the bi-Yang-Baxter deformation parameters.Second, we perform a perturbative expansion of the thermodynamic Bethe ansatz (TBA) equations of the SU(N) λ-model with WZW level k in the presence of a chemical potential. This is done with its exact S-matrix and the recently developed techniques [1, 2] using a Wiener-Hopf decomposition, which involve a careful matching of bulk and edge ans¨atze. We determine the asymptotic expansion of this series and compute its renormalon ambiguities in the Borel plane. The analysis is supplemented by a parallel solution of the TBA equations that results in a transseries. The transseries comes with an ambiguity that is shown to precisely match the Borel ambiguity. It is shown that the leading IR renormalon vanishes when k is a divisor of N. |
published_date |
2023-03-23T15:08:56Z |
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1778290667498242048 |
score |
11.02167 |