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Novel insight into center-vortex geometry in four dimensions
Jackson A. Mickley 
,
Chris Allton ,
Ryan Bignell ,
Derek B. Leinweber
,
Chris Allton ,
Ryan Bignell ,
Derek B. Leinweber
Physical Review D, Volume: 112, Issue: 5
Swansea University Authors:
Chris Allton , Ryan Bignell
-
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DOI (Published version): 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 app...
| Published in: | Physical Review D |
|---|---|
| ISSN: | 2470-0010 2470-0029 |
| Published: |
American Physical Society (APS)
2025
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa71208 |
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2026-01-09T05:32:18Z |
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2026-01-08T10:32:12.4708439 v2 71208 2026-01-08 Novel insight into center-vortex geometry in four dimensions de706a260fa1e1e47430693e135f41c7 0000-0003-0795-124X Chris Allton Chris Allton true false ed4db571151f28021668b4a28b3db4d8 0000-0001-8401-1345 Ryan Bignell Ryan Bignell true false 2026-01-08 BGPS 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. Journal Article Physical Review D 112 5 American Physical Society (APS) 2470-0010 2470-0029 15 9 2025 2025-09-15 10.1103/ptfd-yjtb COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University Other This research was supported by the Australian Research Council through Grant No. DP210103706. C. A. is grateful for support via STFC Grant No. ST/X000648/1 and the award of a Southgate Fellowship from the University of Adelaide. R. B. acknowledges support from a Science Foundation Ireland Frontiers for the Future Project award with Grant No. SFI-21/FFPP/10186. 2026-01-08T10:32:12.4708439 2026-01-08T09:53:02.6585103 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Jackson A. Mickley 0000-0001-5294-2823 1 Chris Allton 0000-0003-0795-124X 2 Ryan Bignell 0000-0001-8401-1345 3 Derek B. Leinweber 0000-0002-4745-6027 4 71208__35919__706a307589964db799a027ab04e83ffa.pdf 71208.VoR.pdf 2026-01-08T09:57:15.5958234 Output 7485369 application/pdf Version of Record true Released under the terms of the Creative Commons Attribution 4.0 International license. true eng https://creativecommons.org/licenses/by/4.0/ |
| title |
Novel insight into center-vortex geometry in four dimensions |
| spellingShingle |
Novel insight into center-vortex geometry in four dimensions Chris Allton Ryan Bignell |
| title_short |
Novel insight into center-vortex geometry in four dimensions |
| title_full |
Novel insight into center-vortex geometry in four dimensions |
| title_fullStr |
Novel insight into center-vortex geometry in four dimensions |
| title_full_unstemmed |
Novel insight into center-vortex geometry in four dimensions |
| title_sort |
Novel insight into center-vortex geometry in four dimensions |
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de706a260fa1e1e47430693e135f41c7 ed4db571151f28021668b4a28b3db4d8 |
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de706a260fa1e1e47430693e135f41c7_***_Chris Allton ed4db571151f28021668b4a28b3db4d8_***_Ryan Bignell |
| author |
Chris Allton Ryan Bignell |
| author2 |
Jackson A. Mickley Chris Allton Ryan Bignell Derek B. Leinweber |
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Journal article |
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Physical Review D |
| container_volume |
112 |
| container_issue |
5 |
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2025 |
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Swansea University |
| issn |
2470-0010 2470-0029 |
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10.1103/ptfd-yjtb |
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American Physical Society (APS) |
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| description |
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. |
| published_date |
2025-09-15T05:34:54Z |
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11.461531 |