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High Energy Physics - Lattice
Title: Topological Data Analysis of Monopoles in $U(1)$ Lattice Gauge Theory
(Submitted on 12 Mar 2024 (v1), last revised 22 Mar 2024 (this version, v2))
Abstract: In $4$-dimensional pure compact $U(1)$ lattice gauge theory, we analyse topological aspects of the dynamics of monopoles across the deconfinement phase transition. We do this using tools from Topological Data Analysis (TDA). We demonstrate that observables constructed from the zeroth and first homology groups of monopole current networks may be used to quantitatively and robustly locate the critical inverse coupling $\beta_{c}$ through finite-size scaling. Our method provides a mathematically robust framework for the characterisation of topological invariants related to monopole currents, putting on firmer ground earlier investigations. Moreover, our approach can be generalised to the study of Abelian monopoles in non-Abelian gauge theories.
Submission history
From: Xavier Crean [view email][v1] Tue, 12 Mar 2024 15:16:40 GMT (149kb,D)
[v2] Fri, 22 Mar 2024 15:27:24 GMT (151kb,D)
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