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Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories

Biagio Lucini Orcid Logo, Xavier Crean Orcid Logo, Jeffrey Giansiracusa

Proceedings of The 41st International Symposium on Lattice Field Theory — PoS(LATTICE2024), Volume: 466, Start page: 395

Swansea University Authors: Biagio Lucini Orcid Logo, Xavier Crean Orcid Logo

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DOI (Published version): 10.22323/1.466.0395

Abstract

Motivated by recent literature on the possible existence of a second higher-temperature phase transition in Quantum Chromodynamics, we revisit the proposal that colour confinement is related to the dynamics of magnetic monopoles using methods of Topological Data Analysis, which provides a mathematic...

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Published in: Proceedings of The 41st International Symposium on Lattice Field Theory — PoS(LATTICE2024)
ISSN: 1824-8039
Published: Trieste, Italy Sissa Medialab 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa69057
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spelling 2025-04-08T10:38:13.0045374 v2 69057 2025-03-06 Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories 7e6fcfe060e07a351090e2a8aba363cf 0000-0001-8974-8266 Biagio Lucini Biagio Lucini true false 02fdd6e1bc74a3aee6538a718f1209ca 0009-0007-8620-6243 Xavier Crean Xavier Crean true false 2025-03-06 MACS Motivated by recent literature on the possible existence of a second higher-temperature phase transition in Quantum Chromodynamics, we revisit the proposal that colour confinement is related to the dynamics of magnetic monopoles using methods of Topological Data Analysis, which provides a mathematically rigorous characterisation of topological properties of quantities defined on a lattice. After introducing persistent homology, one of the main tools in Topological Data Analysis, we shall discuss how this concept can be used to quantitatively analyse the behaviour of monopoles across the deconfinement phase transition. Our approach is first demonstrated for Compact U(1) Lattice Gauge Theory, which is known to have a zero-temperature deconfinement phase transition driven by the restoration of the symmetry associated with the conservation of the magnetic charge. For this system, we perform a finite-size scaling analysis of observables capturing the homology of magnetic current loops, showing that the expected value of the deconfinement critical coupling is reproduced by our analysis. We then extend our method to SU(3) gauge theory, in which Abelian magnetic monopoles are identified after projection in the Maximal Abelian Gauge. A finite-size scaling of our homological observables of Abelian magnetic current loops at temporal size Nt=4 provides the expected value of the critical coupling with an accuracy that is generally higher than that obtained with conventional thermodynamic approaches at comparable statistics, hinting towards the relevance of topological properties of monopole currents for confinement. Conference Paper/Proceeding/Abstract Proceedings of The 41st International Symposium on Lattice Field Theory — PoS(LATTICE2024) 466 395 Sissa Medialab Trieste, Italy 1824-8039 17 2 2025 2025-02-17 10.22323/1.466.0395 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Not Required EPSRC, STFC, Welsh Government: EP/V521917/1, EP/R018472/1, EP/Y028872/1, EP/X017168/1, ST/T000813/1, ST/X000648/1 2025-04-08T10:38:13.0045374 2025-03-06T19:34:10.5753279 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Biagio Lucini 0000-0001-8974-8266 1 Xavier Crean 0009-0007-8620-6243 2 Jeffrey Giansiracusa 3 69057__33756__a23134a2cffe41659f766b95ffe150b7.pdf LATTICE2024_395.pdf 2025-03-06T19:47:35.3690049 Output 705698 application/pdf Version of Record true Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. true eng https://creativecommons.org/licenses/by-nc-nd/4.0/ 309 Biagio Lucini 0000-0001-8974-8266 b.lucini@swansea.ac.uk
title Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories
spellingShingle Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories
Biagio Lucini
Xavier Crean
title_short Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories
title_full Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories
title_fullStr Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories
title_full_unstemmed Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories
title_sort Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories
author_id_str_mv 7e6fcfe060e07a351090e2a8aba363cf
02fdd6e1bc74a3aee6538a718f1209ca
author_id_fullname_str_mv 7e6fcfe060e07a351090e2a8aba363cf_***_Biagio Lucini
02fdd6e1bc74a3aee6538a718f1209ca_***_Xavier Crean
author Biagio Lucini
Xavier Crean
author2 Biagio Lucini
Xavier Crean
Jeffrey Giansiracusa
format Conference Paper/Proceeding/Abstract
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container_start_page 395
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institution Swansea University
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doi_str_mv 10.22323/1.466.0395
publisher Sissa Medialab
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hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
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department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
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description Motivated by recent literature on the possible existence of a second higher-temperature phase transition in Quantum Chromodynamics, we revisit the proposal that colour confinement is related to the dynamics of magnetic monopoles using methods of Topological Data Analysis, which provides a mathematically rigorous characterisation of topological properties of quantities defined on a lattice. After introducing persistent homology, one of the main tools in Topological Data Analysis, we shall discuss how this concept can be used to quantitatively analyse the behaviour of monopoles across the deconfinement phase transition. Our approach is first demonstrated for Compact U(1) Lattice Gauge Theory, which is known to have a zero-temperature deconfinement phase transition driven by the restoration of the symmetry associated with the conservation of the magnetic charge. For this system, we perform a finite-size scaling analysis of observables capturing the homology of magnetic current loops, showing that the expected value of the deconfinement critical coupling is reproduced by our analysis. We then extend our method to SU(3) gauge theory, in which Abelian magnetic monopoles are identified after projection in the Maximal Abelian Gauge. A finite-size scaling of our homological observables of Abelian magnetic current loops at temporal size Nt=4 provides the expected value of the critical coupling with an accuracy that is generally higher than that obtained with conventional thermodynamic approaches at comparable statistics, hinting towards the relevance of topological properties of monopole currents for confinement.
published_date 2025-02-17T05:27:11Z
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