Journal of High Energy Physics

, 2014:101 | Cite as

Vortex zero modes, large flux limit and Ambjørn-Nielsen-Olesen magnetic instabilities

  • Stefano Bolognesi
  • Chandrasekhar Chatterjee
  • Sven Bjarke Gudnason
  • Kenichi Konishi
Open Access
Article

Abstract

In the large flux limit vortices become flux tubes with almost constant magnetic field in the interior region. This occurs in the case of non-Abelian vortices as well, and the study of such configurations allows us to reveal a close relationship between vortex zero modes and the gyromagnetic instabilities of vector bosons in a strong background magnetic field discovered by Nielsen, Olesen and Ambjørn. The BPS vortices are exactly at the onset of this instability, and the dimension of their moduli space is precisely reproduced in this way. We present a unifying picture in which, through the study of the linear spectrum of scalars, fermions and W bosons in the magnetic field background, the expected number of translational, orientational, fermionic as well as semilocal zero modes is correctly reproduced in all cases.

Keywords

Spontaneous Symmetry Breaking Solitons Monopoles and Instantons Nonperturbative Effects Electromagnetic Processes and Properties 

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]
    N.K. Nielsen and P. Olesen, An Unstable Yang-Mills Field Mode, Nucl. Phys. B 144 (1978) 376 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    J. Ambjørn and P. Olesen, On electroweak magnetism, Nucl. Phys. B 315 (1989) 606 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    J. Ambjørn and P. Olesen, A Condensate Solution of the Electroweak Theory Which Interpolates Between the Broken and the Symmetric Phase, Nucl. Phys. B 330 (1990) 193 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    R. Auzzi, S. Bolognesi, J. Evslin, K. Konishi and A. Yung, NonAbelian superconductors: Vortices and confinement in N =2 SQCD, Nucl. Phys. B 673 (2003) 187 [hep-th/0307287] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    A. Hanany and D. Tong, Vortices, instantons and branes, JHEP 07 (2003) 037 [hep-th/0306150] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    M. Shifman and A. Yung, NonAbelian string junctions as confined monopoles, Phys. Rev. D 70 (2004) 045004 [hep-th/0403149] [INSPIRE].ADSGoogle Scholar
  7. [7]
    M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Solitons in the Higgs phase: The Moduli matrix approach, J. Phys. A 39 (2006) R315 [hep-th/0602170] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  8. [8]
    S. Bolognesi, Domain walls and flux tubes, Nucl. Phys. B 730 (2005) 127 [hep-th/0507273] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    S. Bolognesi, Large-N , Z(N) strings and bag models, Nucl. Phys. B 730 (2005) 150 [hep-th/0507286] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    S. Bolognesi and S.B. Gudnason, Multi-vortices are wall vortices: A Numerical proof, Nucl. Phys. B 741 (2006) 1 [hep-th/0512132] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  11. [11]
    S. Bolognesi and S.B. Gudnason, Soliton junctions in the large magnetic flux limit, Nucl. Phys. B 754 (2006) 293 [hep-th/0606065] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    M. Shifman and A. Yung, Non-Abelian semilocal strings in N =2 supersymmetric QCD, Phys. Rev. D 73 (2006) 125012 [hep-th/0603134] [INSPIRE].ADSGoogle Scholar
  13. [13]
    K. Hashimoto and D. Tong, Reconnection of non-Abelian cosmic strings, JCAP 09 (2005) 004 [hep-th/0506022] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    R. Auzzi, M. Shifman and A. Yung, Composite non-Abelian flux tubes in N =2 SQCD, Phys. Rev. D 73 (2006) 105012 [Erratum ibid. D 76 (2007) 109901] [hep-th/0511150] [INSPIRE].
  15. [15]
    M. Eto, K. Konishi, G. Marmorini, M. Nitta, K. Ohashi et al., Non-Abelian Vortices of Higher Winding Numbers, Phys. Rev. D 74 (2006) 065021 [hep-th/0607070] [INSPIRE].ADSMathSciNetGoogle Scholar
  16. [16]
    M. Eto, T. Fujimori, S.B. Gudnason, K. Konishi, T. Nagashima et al., Non-Abelian Vortices in SO(N ) and USp(N ) Gauge Theories, JHEP 06 (2009) 004 [arXiv:0903.4471] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    S.B. Gudnason, Y. Jiang and K. Konishi, Non-Abelian vortex dynamics: Effective world-sheet action, JHEP 08 (2010) 012 [arXiv:1007.2116] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Moduli space of non-Abelian vortices, Phys. Rev. Lett. 96 (2006) 161601 [hep-th/0511088] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    M. Eto, J. Evslin, K. Konishi, G. Marmorini, M. Nitta et al., On the moduli space of semilocal strings and lumps, Phys. Rev. D 76 (2007) 105002 [arXiv:0704.2218] [INSPIRE].ADSMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Stefano Bolognesi
    • 1
    • 2
  • Chandrasekhar Chatterjee
    • 2
    • 1
  • Sven Bjarke Gudnason
    • 3
  • Kenichi Konishi
    • 1
    • 2
  1. 1.Department of PhysicsE. Fermi, University of PisaPisaItaly
  2. 2.INFN, Sezione di PisaPisaItaly
  3. 3.Nordita, KTH Royal Institute of Technology and Stockholm UniversityStockholmSweden

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