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Novel insight into center-vortex geometry in four dimensions
,
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 |
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| ISSN: | 2470-0010 2470-0029 |
| Published: |
American Physical Society (APS)
2025
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa71208 |
| 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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| College: |
Faculty of Science and Engineering |
| Funders: |
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. |
| Issue: |
5 |