Advertisement

Journal of High Energy Physics

, 2015:108 | Cite as

Colorful plane vortices and chiral symmetry breaking in SU(2) lattice gauge theory

  • Seyed Mohsen Hosseini Nejad
  • Manfried Faber
  • Roman Höllwieser
Open Access
Regular Article - Theoretical Physics

Abstract

We investigate plane vortices with color structure. The topological charge and gauge action of such colorful plane vortices are studied in the continuum and on the lattice. These configurations are vacuum to vacuum transitions changing the winding number between the two vacua, leading to a topological charge Q = −1 in the continuum. After growing temporal extent of these vortices, the lattice topological charge approaches −1 and the index theorem is fulfilled. We analyze the low lying modes of the overlap Dirac operator in the background of these colorful plane vortices and compare them with those of spherical vortices. They show characteristic properties for spontaneous chiral symmetry breaking.

Keywords

Spontaneous Symmetry Breaking Lattice Gauge Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    G.K. Savvidy, Infrared Instability of the Vacuum State of Gauge Theories and Asymptotic Freedom, Phys. Lett. B 71 (1977) 133 [INSPIRE].CrossRefADSGoogle Scholar
  2. [2]
    G. ’t Hooft, On the Phase Transition Towards Permanent Quark Confinement, Nucl. Phys. B 138 (1978) 1 [INSPIRE].
  3. [3]
    P. Vinciarelli, Fluxon Solutions in Nonabelian Gauge Models, Phys. Lett. B 78 (1978) 485 [INSPIRE].CrossRefADSGoogle Scholar
  4. [4]
    T. Yoneya, Z(N) Topological Excitations in Yang-Mills Theories: Duality and Confinement, Nucl. Phys. B 144 (1978) 195 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  5. [5]
    J.M. Cornwall, Quark Confinement and Vortices in Massive Gauge Invariant QCD, Nucl. Phys. B 157 (1979) 392 [INSPIRE].CrossRefADSGoogle Scholar
  6. [6]
    G. Mack and V.B. Petkova, Comparison of Lattice Gauge Theories with Gauge Groups Z(2) and SU(2), Annals Phys. 123 (1979) 442 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  7. [7]
    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. B 160 (1979) 380 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  8. [8]
    L. Del Debbio, M. Faber, J. Greensite and Š. Olejník, Center dominance and Z(2) vortices in SU(2) lattice gauge theory, Phys. Rev. D 55 (1997) 2298 [hep-lat/9610005] [INSPIRE].ADSGoogle Scholar
  9. [9]
    T.G. Kovacs and E.T. Tomboulis, Vortices and confinement at weak coupling, Phys. Rev. D 57 (1998) 4054 [hep-lat/9711009] [INSPIRE].ADSGoogle Scholar
  10. [10]
    M. Engelhardt and H. Reinhardt, Center vortex model for the infrared sector of Yang-Mills theory: Confinement and deconfinement, Nucl. Phys. B 585 (2000) 591 [hep-lat/9912003] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  11. [11]
    R. Bertle and M. Faber, Vortices, confinement and Higgs fields, hep-lat/0212027 [INSPIRE].
  12. [12]
    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. B 685 (2004) 227 [hep-lat/0311029] [INSPIRE].CrossRefADSGoogle Scholar
  13. [13]
    R. Hllwieser, D. Altarawneh and M. Engelhardt, Random center vortex lines in continuous 3D space-time, arXiv:1411.7089 [INSPIRE].
  14. [14]
    D. Altarawneh, M. Engelhardt and R. Höllwieser, A model of random center vortex lines in continuous 2+1 dimensional space-time, in preparation (2015).Google Scholar
  15. [15]
    J. Greensite and R. Hllwieser, Double-winding Wilson loops and monopole confinement mechanisms, Phys. Rev. D 91 (2015) 054509 [arXiv:1411.5091] [INSPIRE].ADSGoogle Scholar
  16. [16]
    D. Trewartha, W. Kamleh and D. Leinweber, Connection between centre vortices and instantons through gauge-field smoothing, arXiv:1509.05518 [INSPIRE].
  17. [17]
    R. Bertle, M. Engelhardt and M. Faber, Topological susceptibility of Yang-Mills center projection vortices, Phys. Rev. D 64 (2001) 074504 [hep-lat/0104004] [INSPIRE].ADSGoogle Scholar
  18. [18]
    M. Engelhardt, Center vortex model for the infrared sector of Yang-Mills theory: Topological susceptibility, Nucl. Phys. B 585 (2000) 614 [hep-lat/0004013] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  19. [19]
    M. Engelhardt, Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility, Phys. Rev. D 83 (2011) 025015 [arXiv:1008.4953] [INSPIRE].ADSGoogle Scholar
  20. [20]
    R. Hollwieser, M. Faber and U.M. Heller, Lattice Index Theorem and Fractional Topological Charge, arXiv:1005.1015 [INSPIRE].
  21. [21]
    R. Hollwieser, M. Faber and U.M. Heller, Intersections of thick Center Vortices, Dirac Eigenmodes and Fractional Topological Charge in SU(2) Lattice Gauge Theory, JHEP 06 (2011) 052 [arXiv:1103.2669] [INSPIRE].CrossRefADSGoogle Scholar
  22. [22]
    T. Schweigler, R. Höllwieser, M. Faber and U.M. Heller, Colorful SU(2) center vortices in the continuum and on the lattice, Phys. Rev. D 87 (2013) 054504 [arXiv:1212.3737] [INSPIRE].ADSGoogle Scholar
  23. [23]
    R. Hollwieser, M. Faber and U.M. Heller, Critical analysis of topological charge determination in the background of center vortices in SU(2) lattice gauge theory, Phys. Rev. D 86 (2012) 014513 [arXiv:1202.0929] [INSPIRE].ADSGoogle Scholar
  24. [24]
    R. Höllwieser and M. Engelhardt, Smearing Center Vortices, PoS(LATTICE2014)356 [arXiv:1411.7097] [INSPIRE].
  25. [25]
    R. Höllwieser and M. Engelhardt, Approaching SU(2) gauge dynamics with smeared Z(2) vortices, Phys. Rev. D 92 (2015) 034502 [arXiv:1503.00016] [INSPIRE].ADSGoogle Scholar
  26. [26]
    D. Altarawneh, R. Höllwieser and M. Engelhardt, Confining Bond Rearrangement in the Random Center Vortex Model, arXiv:1508.07596 [INSPIRE].
  27. [27]
    R. Höllwieser and D. Altarawneh, Center Vortices, Area Law and the Catenary Solution, arXiv:1509.00145 [INSPIRE].
  28. [28]
    P. de Forcrand and M. D’Elia, On the relevance of center vortices to QCD, Phys. Rev. Lett. 82 (1999) 4582 [hep-lat/0004013] [INSPIRE].CrossRefADSGoogle Scholar
  29. [29]
    C. Alexandrou, P. de Forcrand and M. D’Elia, The Role of center vortices in QCD, Nucl. Phys. A 663 (2000) 1031 [hep-lat/9909005] [INSPIRE].CrossRefADSGoogle Scholar
  30. [30]
    M. Engelhardt and H. Reinhardt, Center projection vortices in continuum Yang-Mills theory, Nucl. Phys. B567 (2000) 249 [hep-lat/9907139] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  31. [31]
    S.-S. Xue, The Standard model and parity conservation, Nucl. Phys. Proc. Suppl. 94 (2001) 781 [hep-lat/0010031] [INSPIRE].CrossRefADSGoogle Scholar
  32. [32]
    M. Engelhardt, Center vortex model for the infrared sector of Yang-Mills theory: Quenched Dirac spectrum and chiral condensate, Nucl. Phys. B 638 (2002) 81 [hep-lat/0204002] [INSPIRE].MATHMathSciNetCrossRefADSGoogle Scholar
  33. [33]
    D. Leinweber et al., Role of centre vortices in dynamical mass generation, Nucl. Phys. Proc. Suppl. 161 (2006) 130.CrossRefADSGoogle Scholar
  34. [34]
    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 (2008) 074507 [arXiv:0708.3335] [INSPIRE].ADSGoogle Scholar
  35. [35]
    R. Höllwieser, M. Faber, J. Greensite, U.M. Heller and Š. Olejník, Center Vortices and the Dirac Spectrum, Phys. Rev. D 78 (2008) 054508 [arXiv:0805.1846] [INSPIRE].ADSGoogle Scholar
  36. [36]
    R. Höllwieser, Center vortices and chiral symmetry breaking, PhD thesis, Vienna, Tech. U., Atominst., 2009-01-11, http://katalog.ub.tuwien.ac.at/AC05039934.
  37. [37]
    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 (2011) 034501 [arXiv:1010.4624] [INSPIRE].ADSGoogle Scholar
  38. [38]
    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 (2013) 114505 [arXiv:1304.1277] [INSPIRE].ADSGoogle Scholar
  39. [39]
    N. Brambilla et al., QCD and Strongly Coupled Gauge Theories: Challenges and Perspectives, Eur. Phys. J. C 74 (2014) 2981 [arXiv:1404.3723] [INSPIRE].CrossRefGoogle Scholar
  40. [40]
    R. Höllwieser, M. Faber, T. Schweigler and U.M. Heller, Chiral Symmetry Breaking from Center Vortices, arXiv:1410.2333 [INSPIRE].
  41. [41]
    D. Trewartha, W. Kamleh and D. Leinweber, Centre Vortex Effects on the Overlap Quark Propagator, PoS(LATTICE2014)357 [arXiv:1411.0766] [INSPIRE].
  42. [42]
    D. Trewartha, W. Kamleh and D. Leinweber, Evidence that centre vortices underpin dynamical chiral symmetry breaking in SU(3) gauge theory, Phys. Lett. B 747 (2015) 373 [arXiv:1502.06753] [INSPIRE].CrossRefADSGoogle Scholar
  43. [43]
    R. Bertle, M. Faber, J. Greensite and Š. Olejník, The Structure of projected center vortices in lattice gauge theory, JHEP 03 (1999) 019 [hep-lat/9903023] [INSPIRE].CrossRefADSGoogle Scholar
  44. [44]
    H. Reinhardt and M. Engelhardt, Center vortices in continuum Yang-Mills theory, hep-th/0010031 [INSPIRE].
  45. [45]
    T. Banks and A. Casher, Chiral Symmetry Breaking in Confining Theories, Nucl. Phys. B 169 (1980) 103 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  46. [46]
    G. Jordan, R. Höllwieser, M. Faber and U.M. Heller, Tests of the lattice index theorem, Phys. Rev. D 77 (2008) 014515 [arXiv:0710.5445] [INSPIRE].ADSGoogle Scholar
  47. [47]
    D. Diakonov, Instantons at work, Prog. Part. Nucl. Phys. 51 (2003) 173 [hep-ph/0212026] [INSPIRE].CrossRefADSGoogle Scholar
  48. [48]
    M.F. Atiyah and I.M. Singer, The Index of elliptic operators. 5, Annals Math. 93 (1971) 139.MathSciNetCrossRefGoogle Scholar
  49. [49]
    A.S. Schwarz, On Regular Solutions of Euclidean Yang-Mills Equations, Phys. Lett. B 67 (1977) 172 [INSPIRE].CrossRefADSGoogle Scholar
  50. [50]
    L.S. Brown, R.D. Carlitz and C.-k. Lee, Massless Excitations in Instanton Fields, Phys. Rev. D 16 (1977) 417 [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Seyed Mohsen Hosseini Nejad
    • 1
  • Manfried Faber
    • 2
  • Roman Höllwieser
    • 2
    • 3
  1. 1.Department of PhysicsUniversity of TehranTehranIran
  2. 2.Institute of Atomic and Subatomic PhysicsVienna University of TechnologyViennaAustria
  3. 3.Department of PhysicsNew Mexico State UniversityLas CrucesU.S.A.

Personalised recommendations