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Resurgence in η-deformed Principal Chiral Models

Saskia Demulder, Daniele Dorigoni, Daniel Thompson Orcid Logo

Journal of High Energy Physics, Volume: 2016, Issue: 7

Swansea University Author: Daniel Thompson Orcid Logo

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DOI (Published version): 10.1007/jhep07(2016)088

Abstract

We study the SU(2) Principal Chiral Model (PCM) in the presence of an integrable η-deformation. We put the theory on R×S1 with twisted boundary conditions and then reduce the circle to obtain an effective quantum mechanics associated with the Whittaker-Hill equation. Using resurgent analysis we stud...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: Springer Science and Business Media LLC 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa33814
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first_indexed 2017-05-22T14:03:18Z
last_indexed 2020-07-29T18:52:16Z
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spelling 2020-07-29T16:04:46.2574416 v2 33814 2017-05-22 Resurgence in η-deformed Principal Chiral Models 9c8715ee44a574eda1194c9808d99c62 0000-0001-8319-8275 Daniel Thompson Daniel Thompson true false 2017-05-22 SPH We study the SU(2) Principal Chiral Model (PCM) in the presence of an integrable η-deformation. We put the theory on R×S1 with twisted boundary conditions and then reduce the circle to obtain an effective quantum mechanics associated with the Whittaker-Hill equation. Using resurgent analysis we study the large order behaviour of perturbation theory and recover the fracton events responsible for IR renormalons. The fractons are modified from the standard PCM due to the presence of this η-deformation but they are still the constituents of uniton-like solutions in the deformed quantum field theory. We also find novel SL(2,ℂ) saddles, thus strengthening the conjecture that the semi-classical expansion of the path integral gives rise to a resurgent transseries once written as a sum over Lefschetz thimbles living in a complexification of the field space. We conclude by connecting our quantum mechanics to a massive deformation of the N=2 4-d gauge theory with gauge group SU(2) and Nf=2. Journal Article Journal of High Energy Physics 2016 7 Springer Science and Business Media LLC 1029-8479 Nonperturbative Effects; Sigma Models; Integrable Field Theories; Solitons Monopoles and Instantons 18 7 2016 2016-07-18 10.1007/jhep07(2016)088 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2020-07-29T16:04:46.2574416 2017-05-22T09:57:47.3093179 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Saskia Demulder 1 Daniele Dorigoni 2 Daniel Thompson 0000-0001-8319-8275 3 0033814-07072017110931.pdf 10.10072FJHEP07(2016)088.pdf 2017-07-07T11:09:31.7170000 Output 2792086 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution License (CC-BY 4.0). true eng http://creativecommons.org/licenses/by/4.0/
title Resurgence in η-deformed Principal Chiral Models
spellingShingle Resurgence in η-deformed Principal Chiral Models
Daniel Thompson
title_short Resurgence in η-deformed Principal Chiral Models
title_full Resurgence in η-deformed Principal Chiral Models
title_fullStr Resurgence in η-deformed Principal Chiral Models
title_full_unstemmed Resurgence in η-deformed Principal Chiral Models
title_sort Resurgence in η-deformed Principal Chiral Models
author_id_str_mv 9c8715ee44a574eda1194c9808d99c62
author_id_fullname_str_mv 9c8715ee44a574eda1194c9808d99c62_***_Daniel Thompson
author Daniel Thompson
author2 Saskia Demulder
Daniele Dorigoni
Daniel Thompson
format Journal article
container_title Journal of High Energy Physics
container_volume 2016
container_issue 7
publishDate 2016
institution Swansea University
issn 1029-8479
doi_str_mv 10.1007/jhep07(2016)088
publisher Springer Science and Business Media LLC
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 We study the SU(2) Principal Chiral Model (PCM) in the presence of an integrable η-deformation. We put the theory on R×S1 with twisted boundary conditions and then reduce the circle to obtain an effective quantum mechanics associated with the Whittaker-Hill equation. Using resurgent analysis we study the large order behaviour of perturbation theory and recover the fracton events responsible for IR renormalons. The fractons are modified from the standard PCM due to the presence of this η-deformation but they are still the constituents of uniton-like solutions in the deformed quantum field theory. We also find novel SL(2,ℂ) saddles, thus strengthening the conjecture that the semi-classical expansion of the path integral gives rise to a resurgent transseries once written as a sum over Lefschetz thimbles living in a complexification of the field space. We conclude by connecting our quantum mechanics to a massive deformation of the N=2 4-d gauge theory with gauge group SU(2) and Nf=2.
published_date 2016-07-18T03:41:54Z
_version_ 1763751928091639808
score 11.013371

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