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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G.K. Savvidy, Infrared Instability of the Vacuum State of Gauge Theories and Asymptotic Freedom, Phys. Lett. B 71 (1977) 133 [INSPIRE].
G. ’t Hooft, On the Phase Transition Towards Permanent Quark Confinement, Nucl. Phys. B 138 (1978) 1 [INSPIRE].
P. Vinciarelli, Fluxon Solutions in Nonabelian Gauge Models, Phys. Lett. B 78 (1978) 485 [INSPIRE].
T. Yoneya, Z(N) Topological Excitations in Yang-Mills Theories: Duality and Confinement, Nucl. Phys. B 144 (1978) 195 [INSPIRE].
J.M. Cornwall, Quark Confinement and Vortices in Massive Gauge Invariant QCD, Nucl. Phys. B 157 (1979) 392 [INSPIRE].
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].
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].
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].
T.G. Kovacs and E.T. Tomboulis, Vortices and confinement at weak coupling, Phys. Rev. D 57 (1998) 4054 [hep-lat/9711009] [INSPIRE].
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].
R. Bertle and M. Faber, Vortices, confinement and Higgs fields, hep-lat/0212027 [INSPIRE].
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].
R. Hllwieser, D. Altarawneh and M. Engelhardt, Random center vortex lines in continuous 3D space-time, arXiv:1411.7089 [INSPIRE].
D. Altarawneh, M. Engelhardt and R. Höllwieser, A model of random center vortex lines in continuous 2+1 dimensional space-time, in preparation (2015).
J. Greensite and R. Hllwieser, Double-winding Wilson loops and monopole confinement mechanisms, Phys. Rev. D 91 (2015) 054509 [arXiv:1411.5091] [INSPIRE].
D. Trewartha, W. Kamleh and D. Leinweber, Connection between centre vortices and instantons through gauge-field smoothing, arXiv:1509.05518 [INSPIRE].
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].
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].
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].
R. Hollwieser, M. Faber and U.M. Heller, Lattice Index Theorem and Fractional Topological Charge, arXiv:1005.1015 [INSPIRE].
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].
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].
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].
R. Höllwieser and M. Engelhardt, Smearing Center Vortices, PoS(LATTICE2014)356 [arXiv:1411.7097] [INSPIRE].
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].
D. Altarawneh, R. Höllwieser and M. Engelhardt, Confining Bond Rearrangement in the Random Center Vortex Model, arXiv:1508.07596 [INSPIRE].
R. Höllwieser and D. Altarawneh, Center Vortices, Area Law and the Catenary Solution, arXiv:1509.00145 [INSPIRE].
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].
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].
M. Engelhardt and H. Reinhardt, Center projection vortices in continuum Yang-Mills theory, Nucl. Phys. B567 (2000) 249 [hep-lat/9907139] [INSPIRE].
S.-S. Xue, The Standard model and parity conservation, Nucl. Phys. Proc. Suppl. 94 (2001) 781 [hep-lat/0010031] [INSPIRE].
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].
D. Leinweber et al., Role of centre vortices in dynamical mass generation, Nucl. Phys. Proc. Suppl. 161 (2006) 130.
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].
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].
R. Höllwieser, Center vortices and chiral symmetry breaking, PhD thesis, Vienna, Tech. U., Atominst., 2009-01-11, http://katalog.ub.tuwien.ac.at/AC05039934.
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].
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].
N. Brambilla et al., QCD and Strongly Coupled Gauge Theories: Challenges and Perspectives, Eur. Phys. J. C 74 (2014) 2981 [arXiv:1404.3723] [INSPIRE].
R. Höllwieser, M. Faber, T. Schweigler and U.M. Heller, Chiral Symmetry Breaking from Center Vortices, arXiv:1410.2333 [INSPIRE].
D. Trewartha, W. Kamleh and D. Leinweber, Centre Vortex Effects on the Overlap Quark Propagator, PoS(LATTICE2014)357 [arXiv:1411.0766] [INSPIRE].
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].
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].
H. Reinhardt and M. Engelhardt, Center vortices in continuum Yang-Mills theory, hep-th/0010031 [INSPIRE].
T. Banks and A. Casher, Chiral Symmetry Breaking in Confining Theories, Nucl. Phys. B 169 (1980) 103 [INSPIRE].
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].
D. Diakonov, Instantons at work, Prog. Part. Nucl. Phys. 51 (2003) 173 [hep-ph/0212026] [INSPIRE].
M.F. Atiyah and I.M. Singer, The Index of elliptic operators. 5, Annals Math. 93 (1971) 139.
A.S. Schwarz, On Regular Solutions of Euclidean Yang-Mills Equations, Phys. Lett. B 67 (1977) 172 [INSPIRE].
L.S. Brown, R.D. Carlitz and C.-k. Lee, Massless Excitations in Instanton Fields, Phys. Rev. D 16 (1977) 417 [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1508.01042
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Nejad, S.M.H., Faber, M. & Höllwieser, R. Colorful plane vortices and chiral symmetry breaking in SU(2) lattice gauge theory. J. High Energ. Phys. 2015, 108 (2015). https://doi.org/10.1007/JHEP10(2015)108
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2015)108