Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917792492552192 |
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| author | Crean, Xavier Giansiracusa, Jeffrey Lucini, Biagio |
| author_facet | Crean, Xavier Giansiracusa, Jeffrey Lucini, Biagio |
| contents | 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 $β_{c}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07739 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory Crean, Xavier Giansiracusa, Jeffrey Lucini, Biagio High Energy Physics - Lattice Statistical Mechanics High Energy Physics - Theory Algebraic Topology 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 $β_{c}$ 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. |
| title | Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory |
| topic | High Energy Physics - Lattice Statistical Mechanics High Energy Physics - Theory Algebraic Topology |
| url | https://arxiv.org/abs/2403.07739 |