Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories TDA of Abelian Magnetic Monopoles

Crean, Xavier; Giansiracusa, Jeffrey; Lucini, Biagio

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 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 N_t = 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.

Citation

Crean, X., Giansiracusa, J., & Lucini, B. (2024, July). Topological Data Analysis of Abelian Magnetic Monopoles in Gauge Theories TDA of Abelian Magnetic Monopoles. Presented at The 41st International Symposium on Lattice Field Theory (LATTICE2024), Liverpool, UK

• Presentation Conference Type: Conference Paper (published)
• Conference Name: The 41st International Symposium on Lattice Field Theory (LATTICE2024)
• Start Date: Jul 28, 2024
• End Date: Aug 3, 2024
• Acceptance Date: Jul 28, 2024
• Online Publication Date: Aug 3, 2024
• Publication Date: Aug 3, 2024
• Deposit Date: Feb 20, 2025
• Publicly Available Date: Feb 21, 2025
• Peer Reviewed: Peer Reviewed
• Series Title: Proceedings of Science
• Series Number: 395
• Book Title: The 41st International Symposium on Lattice Field Theory (LATTICE2024)
• Public URL: https://durham-repository.worktribe.com/output/3491621
• Publisher URL: https://pos.sissa.it/466/