No Cover Image

E-Thesis 457 views 166 downloads

Resurgence in Deformed Integrable Models / LUCAS SCHEPERS

Swansea University Author: LUCAS SCHEPERS

  • 2023_Schepers_L.final.63254.pdf

    PDF | E-Thesis – open access

    Copyright: The Author, Lucas Schepers, 2023. Distributed under the terms of a Creative Commons Attribution 4.0 License (CC BY 4.0).

    Download (7.52MB)

DOI (Published version): 10.23889/SUthesis.63254

Abstract

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...

Full description

Published: Swansea, Wales, UK 2023
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
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2023-04-26T12:14:11Z
last_indexed 2023-04-26T12:14:11Z
id cronfa63254
recordtype RisThesis
fullrecord <?xml version="1.0" encoding="utf-8"?><rfc1807 xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><bib-version>v2</bib-version><id>63254</id><entry>2023-04-26</entry><title>Resurgence in Deformed Integrable Models</title><swanseaauthors><author><sid>c486fffc20b25838678b537dd15ed78c</sid><firstname>LUCAS</firstname><surname>SCHEPERS</surname><name>LUCAS SCHEPERS</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2023-04-26</date><abstract>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.</abstract><type>E-Thesis</type><journal/><volume/><journalNumber/><paginationStart/><paginationEnd/><publisher/><placeOfPublication>Swansea, Wales, UK</placeOfPublication><isbnPrint/><isbnElectronic/><issnPrint/><issnElectronic/><keywords>Integrable Models, Resurgence, Deformations</keywords><publishedDay>23</publishedDay><publishedMonth>3</publishedMonth><publishedYear>2023</publishedYear><publishedDate>2023-03-23</publishedDate><doi>10.23889/SUthesis.63254</doi><url/><notes/><college>COLLEGE NANME</college><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><supervisor>Thompson, Daniel C. and Nunez, Carlos.</supervisor><degreelevel>Doctoral</degreelevel><degreename>Ph.D</degreename><degreesponsorsfunders>The Royal Society (RGF\R1\180087)</degreesponsorsfunders><apcterm/><funders/><projectreference/><lastEdited>2023-09-28T15:08:55.5379637</lastEdited><Created>2023-04-26T12:36:43.9104550</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Biosciences, Geography and Physics - Physics</level></path><authors><author><firstname>LUCAS</firstname><surname>SCHEPERS</surname><order>1</order></author></authors><documents><document><filename>63254__27215__0798ad80f5504d13a8d93b346f60a321.pdf</filename><originalFilename>2023_Schepers_L.final.63254.pdf</originalFilename><uploaded>2023-04-26T13:12:36.5575955</uploaded><type>Output</type><contentLength>7888469</contentLength><contentType>application/pdf</contentType><version>E-Thesis – open access</version><cronfaStatus>true</cronfaStatus><documentNotes>Copyright: The Author, Lucas Schepers, 2023. 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>
spelling 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
author2 LUCAS SCHEPERS
format E-Thesis
publishDate 2023
institution Swansea University
doi_str_mv 10.23889/SUthesis.63254
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
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
_version_ 1778290667498242048
score 11.03559

Similar Items