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Topological data analysis of the deconfinement transition in SU(3) lattice gauge theory

Daniel Spitz1,*, Julian M. Urban2,3, and Jan M. Pawlowski4,5

  • *Contact author: daniel.spitz@mis.mpg.de
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Phys. Rev. D 111, 114519 – Published 25 June, 2025

DOI: https://doi.org/10.1103/k2xs-4y67

Abstract

We study the confining and deconfining phases of pure SU(3) lattice gauge theory with topological data analysis. This provides unique insights into long range correlations of field configurations across the confinement-deconfinement transition. Specifically, we analyze nontrivial structures in electric and magnetic field energy densities as well as Polyakov loop traces and a Polyakov loop-based variant of the topological density. The Betti curves for filtrations based on the electric and magnetic field energy densities reveal signals of electromagnetic dualities. These dualities can be associated with an interchange in the roles of local lumps of electric and magnetic energy densities around the phase transition. Moreover, we show that plaquette susceptibilities can manifest in the geometric features captured by the Betti curves. We also compare these findings against earlier results for SU(2) and elaborate on the significant differences. Our results demonstrate that topological data analysis can identify clear differences between phase transitions of first and second order for non-Abelian lattice gauge theories and provides unprecedented insights into the relevant structures in their vicinity.

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Phys. Rev. D 111, 114519– Published 25 June, 2025
  • Received 22 December 2024
  • Accepted 2 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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