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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
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...
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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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| 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. |
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| Keywords: |
Integrable Models, Resurgence, Deformations |
| College: |
Faculty of Science and Engineering |