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Novel insight into center-vortex geometry in four dimensions

Jackson A. Mickley1, Chris Allton2,3, Ryan Bignell4, and Derek B. Leinweber1

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Phys. Rev. D 112, 054505 – Published 15 September, 2025

DOI: https://doi.org/10.1103/ptfd-yjtb

Abstract

Center-vortex surfaces are mapped out in four dimensions within the framework of SU(3) lattice gauge theory to understand the role of secondary loops that develop in three-dimensional visualizations of center-vortex structure, appearing separate from the percolating cluster. Loops that initially appear disconnected in three-dimensional slices can originate from the same connected surface in four dimensions depending on the surface’s curvature. For the first time, these secondary loops are identified as “connected” or “disconnected” with respect to the vortex sheet, allowing new insight into the evolution of center-vortex geometry through the finite-temperature phase transition. At low temperatures, we find that secondary loops of any length primarily lie in the same sheet percolating the four-dimensional volume. Only a handful of small secondary sheets disconnected from the percolating sheet are identified. Above the phase transition, the vortex structure is still found to be dominated by a single large sheet but one that has aligned with the temporal dimension. With the near absence of any curvature orthogonal to the temporal dimension, connected secondary loops become vanishingly rare. Other novel quantities, such as the four-dimensional density of secondary sheets and the sheet sizes themselves, are analyzed to build a complete picture of center-vortex geometry in four dimensions.

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Phys. Rev. D 112, 054505– Published 15 September, 2025
  • Received 24 July 2025
  • Accepted 28 August 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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