- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Center vortices in the novel phase of staggered fermions

Jackson A. Mickley1, Derek B. Leinweber1, and Daniel Nogradi2

PDF

Phys. Rev. D 112, 034513 – Published 28 August, 2025

DOI: https://doi.org/10.1103/qhwc-4k7c

Abstract

The geometry of center vortices is studied in the novel lattice-artefact phase that appears with staggered fermions to elucidate any insight provided by the center-vortex degrees of freedom. For various numbers of fermion flavors, the single-site shift symmetry of the staggered-fermion action is broken in a finite region of the (β,m) phase space. Simulations are performed with six degenerate fermion flavors and a range of β values that span the phase boundary. Center vortices are demonstrated to capture the broken shift symmetry that manifests in the unphysical phase. This persists at the level of each individual plaquette orientation, where it is revealed that only the plaquettes that span the broken dimension are affected. Several bulk center-vortex quantities, including the vortex and branching point densities, are considered to highlight other aspects of vortex geometry sensitive to the unphysical phase. A slight preference for the plaquettes affected by the broken shift symmetry to be pierced by a vortex is observed. This translates also to a greater branching point density in three-dimensional slices that span the broken dimension. Combined, these findings provide a novel characterization of the unphysical phase in terms of the fundamental center degrees of freedom.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (57)

  1. W.-J. Lee and S. R. Sharpe, Partial flavor symmetry restoration for chiral staggered fermions, Phys. Rev. D 60, 114503 (1999).
  2. C. Aubin and Q.-H. Wang, Possible Aoki phase for staggered fermions, Phys. Rev. D 70, 114504 (2004).
  3. A. Cheng, A. Hasenfratz, and D. Schaich, Novel phase in SU(3) lattice gauge theory with 12 light fermions, Phys. Rev. D 85, 094509 (2012).
  4. A. Hasenfratz, Y. Shamir, and B. Svetitsky, Taming lattice artifacts with Pauli-Villars fields, Phys. Rev. D 104, 074509 (2021).
  5. A. Y. Kotov, D. Nogradi, K. K. Szabo, and L. Szikszai, More on the flavor dependence of mϱ/fπ, J. High Energy Phys. 07 (2021) 202; 06 (2022) 032.
  6. C. Aubin, K. Colletti, and G. Davila, Unphysical phases in staggered chiral perturbation theory, Phys. Rev. D 93, 085009 (2016).
  7. M. F. L. Golterman and J. Smit, Self-energy and flavor interpretation of staggered fermions, Nucl. Phys. B245, 61 (1984).
  8. G. ’t Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B138, 1 (1978).
  9. G. ’t Hooft, A property of electric and magnetic flux in non-Abelian gauge theories, Nucl. Phys. B153, 141 (1979).
  10. H. B. Nielsen and P. Olesen, A quantum liquid model for the QCD vacuum: Gauge and rotational invariance of domained and quantized homogeneous color fields, Nucl. Phys. B160, 380 (1979).
  11. J. Greensite, The confinement problem in lattice gauge theory, Prog. Part. Nucl. Phys. 51, 1 (2003).
  12. L. Del Debbio, M. Faber, J. Greensite, and Š. Olejník, Center dominance and Z2 vortices in SU(2) lattice gauge theory, Phys. Rev. D 55, 2298 (1997).
  13. L. Del Debbio, M. Faber, J. Greensite, and Š. Olejník, Center vortices and the asymptotic string tension, Nucl. Phys. B, Proc. Suppl. 63, 552 (1998).
  14. K. Langfeld, H. Reinhardt, and O. Tennert, Confinement and scaling of the vortex vacuum of SU(2) lattice gauge theory, Phys. Lett. B 419, 317 (1998).
  15. L. Del Debbio, M. Faber, J. Giedt, J. Greensite, and Š. Olejník, Detection of center vortices in the lattice Yang-Mills vacuum, Phys. Rev. D 58, 094501 (1998).
  16. M. Faber, J. Greensite, and Š. Olejník, Casimir scaling from center vortices: Towards an understanding of the adjoint string tension, Phys. Rev. D 57, 2603 (1998).
  17. M. Faber, J. Greensite, and Š. Olejník, Evidence for a center vortex origin of the adjoint string tension, Acta Phys. Slovaca 49, 177 (1999), http://www.physics.sk/aps/pub.php?y=1999&pub=aps-99-02.
  18. T. G. Kovács and E. T. Tomboulis, Vortices and confinement at weak coupling, Phys. Rev. D 57, 4054 (1998).
  19. K. Langfeld, O. Tennert, M. Engelhardt, and H. Reinhardt, Center vortices of Yang-Mills theory at finite temperatures, Phys. Lett. B 452, 301 (1999).
  20. M. Engelhardt, K. Langfeld, H. Reinhardt, and O. Tennert, Interaction of confining vortices in SU(2) lattice gauge theory, Phys. Lett. B 431, 141 (1998).
  21. R. Bertle, M. Faber, J. Greensite, and Š. Olejník, The structure of projected center vortices in lattice gauge theory, J. High Energy Phys. 03 (1999) 019.
  22. M. Engelhardt, K. Langfeld, H. Reinhardt, and O. Tennert, Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition, Phys. Rev. D 61, 054504 (2000).
  23. M. Engelhardt and H. Reinhardt, Center vortex model for the infrared sector of Yang-Mills theory—confinement and deconfinement, Nucl. Phys. B585, 591 (2000).
  24. M. Faber, J. Greensite, and Š. Olejník, First evidence for center dominance in SU(3) lattice gauge theory, Phys. Lett. B 474, 177 (2000).
  25. P. de Forcrand and M. D’Elia, Relevance of center vortices to QCD, Phys. Rev. Lett. 82, 4582 (1999).
  26. P. de Forcrand and M. Pepe, Center vortices and monopoles without lattice Gribov copies, Nucl. Phys. B598, 557 (2001).
  27. T. G. Kovács and E. T. Tomboulis, Computation of the vortex free energy in SU(2) gauge theory, Phys. Rev. Lett. 85, 704 (2000).
  28. K. Langfeld, H. Reinhardt, and J. Gattnar, Gluon propagator and quark confinement, Nucl. Phys. B621, 131 (2002).
  29. K. Langfeld, Vortex structures in pure SU(3) lattice gauge theory, Phys. Rev. D 69, 014503 (2004).
  30. M. Engelhardt, M. Quandt, and H. Reinhardt, Center vortex model for the infrared sector of SU(3) Yang-Mills theory—Confinement and deconfinement, Nucl. Phys. B685, 227 (2004).
  31. J. Gattnar, C. Gattringer, K. Langfeld, H. Reinhardt, A. Schäfer, S. Solbrig, and T. Tok, Center vortices and Dirac eigenmodes in SU(2) lattice gauge theory, Nucl. Phys. B716, 105 (2005).
  32. V. G. Bornyakov, E. M. Ilgenfritz, B. V. Martemyanov, S. M. Morozov, M. Muller-Preussker, and A. I. Veselov, Interrelation between monopoles, vortices, topological charge and chiral symmetry breaking: Analysis using overlap fermions for SU(2), Phys. Rev. D 77, 074507 (2008).
  33. P. O. Bowman, K. Langfeld, D. B. Leinweber, A. O’Cais, A. Sternbeck, L. von Smekal, and A. G. Williams, Center vortices and the quark propagator in SU(2) gauge theory, Phys. Rev. D 78, 054509 (2008).
  34. P. O. Bowman, K. Langfeld, D. B. Leinweber, A. Sternbeck, L. von Smekal, and A. G. Williams, Role of center vortices in chiral symmetry breaking in SU(3) gauge theory, Phys. Rev. D 84, 034501 (2011).
  35. E.-A. O’Malley, W. Kamleh, D. Leinweber, and P. Moran, SU(3) centre vortices underpin confinement and dynamical chiral symmetry breaking, Phys. Rev. D 86, 054503 (2012).
  36. R. Höllwieser, T. Schweigler, M. Faber, and U. M. Heller, Center vortices and chiral symmetry breaking in SU(2) lattice gauge theory, Phys. Rev. D 88, 114505 (2013).
  37. R. Höllwieser, M. Faber, T. Schweigler, and U. M. Heller, Chiral symmetry breaking from center vortices, Proc. Sci. LATTICE2013 (2014) 505 [arXiv:1410.2333].
  38. A. Trewartha, W. Kamleh, and D. Leinweber, Evidence that centre vortices underpin dynamical chiral symmetry breaking in SU(3) gauge theory, Phys. Lett. B 747, 373 (2015).
  39. J. Greensite, Confinement from center vortices: A review of old and new results, EPJ Web Conf. 137, 01009 (2017).
  40. A. Trewartha, W. Kamleh, and D. Leinweber, Centre vortex removal restores chiral symmetry, J. Phys. G 44, 125002 (2017).
  41. J. C. Biddle, W. Kamleh, and D. B. Leinweber, Static quark potential from center vortices in the presence of dynamical fermions, Phys. Rev. D 106, 054505 (2022).
  42. J. C. Biddle, W. Kamleh, and D. B. Leinweber, Impact of dynamical fermions on the center vortex gluon propagator, Phys. Rev. D 106, 014506 (2022).
  43. J. A. Mickley, W. Kamleh, and D. B. Leinweber, Center vortex geometry at finite temperature, Phys. Rev. D 110, 034516 (2024).
  44. J. A. Mickley, C. Allton, R. Bignell, and D. B. Leinweber, Centre vortex evidence for a second finite-temperature QCD transition, Phys. Rev. D 111, 034508 (2025).
  45. J. A. Mickley, D. B. Leinweber, and D. Nogradi, Center vortices and the SU(3) conformal window, Phys. Rev. D 111, 034516 (2025).
  46. A. Montero, Study of SU(3) vortex-like configurations with a new maximal center gauge fixing method, Phys. Lett. B 467, 106 (1999).
  47. M. Faber, J. Greensite, Š. Olejník, and D. Yamada, The vortex-finding property of maximal center (and other) gauges, J. High Energy Phys. 12 (1999) 012.
  48. S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth, Hybrid Monte Carlo, Phys. Lett. B 195, 216 (1987).
  49. M. A. Clark and A. D. Kennedy, Accelerating dynamical-fermion computations using the rational hybrid Monte Carlo algorithm with multiple pseudofermion fields, Phys. Rev. Lett. 98, 051601 (2007).
  50. C. Morningstar and M. J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D 69, 054501 (2004).
  51. S. Durr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K. K. Szabo, and G. Vulvert (BMW Collaboration), Lattice QCD at the physical point: Simulation and analysis details, J. High Energy Phys. 08 (2011) 148.
  52. K. Symanzik, Continuum limit and improved action in lattice theories: (I). Principles and ϕ4 theory, Nucl. Phys. B226, 187 (1983).
  53. K. Symanzik, Continuum limit and improved action in lattice theories: (II). O(N) non-linear sigma model in perturbation theory, Nucl. Phys. B226, 205 (1983).
  54. D. Nogradi, D. Nogradi, L. Szikszai, and L. Szikszai, The flavor dependence of mϱ/fπ, J. High Energy Phys. 05 (2019) 197; 06 (2022) 031(E).
  55. D. Nogradi and L. Szikszai, The model dependence of mϱ/fπ, Proc. Sci. LATTICE2019 (2019) 237 [arXiv:1912.04114].
  56. J. C. Biddle, W. Kamleh, and D. B. Leinweber, Visualization of center vortex structure, Phys. Rev. D 102, 034504 (2020).
  57. J. C. Biddle, W. Kamleh, and D. B. Leinweber, Center vortex structure in the presence of dynamical fermions, Phys. Rev. D 107, 094507 (2023).

Outline

Information

Phys. Rev. D 112, 034513– Published 28 August, 2025
  • Received 9 June 2025
  • Accepted 12 August 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation