NonAbelian vortices, large winding limits and Aharonov-Bohm effects

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Regular Article - Theoretical Physics


Remarkable simplification arises from considering vortex equations in the large winding limit. This was recently used [1] to display all sorts of vortex zeromodes, the orientational, translational, fermionic as well as semi-local, and to relate them to the apparently distinct phenomena of the Nielsen-Olesen-Ambjorn magnetic instabilities. Here we extend these analyses to more general types of BPS nonAbelian vortices, taking as a prototype a system with gauged U0(1) × SU(N ) × SU r (N ) symmetry where the VEV of charged scalar fields in the bifundamental representation breaks the symmetry to SU(N )ℓ+r . The presence of the massless SU(N )ℓ+r gauge fields in 4D bulk introduces all sorts of non-local, topological phenomena such as the nonAbelian Aharonov-Bohm effects, which in the theory with global SU r (N ) group (g r = 0) are washed away by the strongly fluctuating orientational zeromodes in the worldsheet. Physics changes qualitatively at the moment the right gauge coupling constant gr is turned on.


Duality in Gauge Field Theories Solitons Monopoles and Instantons Nonperturbative Effects Topological States of Matter 


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  1. [1]
    S. Bolognesi, C. Chatterjee, S.B. Gudnason and K. Konishi, Vortex zero modes, large flux limit and Ambjørn-Nielsen-Olesen magnetic instabilities, JHEP 10 (2014) 101 [arXiv:1408.1572] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    S. Bolognesi, Domain walls and flux tubes, Nucl. Phys. B 730 (2005) 127 [hep-th/0507273] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    S. Bolognesi, Large-N , Z(N ) strings and bag models, Nucl. Phys. B 730 (2005) 150 [hep-th/0507286] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    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
  5. [5]
    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
  6. [6]
    A. Hanany and D. Tong, Vortices, instantons and branes, JHEP 07 (2003) 037 [hep-th/0306150] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    M. Shifman and A. Yung, NonAbelian string junctions as confined monopoles, Phys. Rev. D 70 (2004) 045004 [hep-th/0403149] [INSPIRE].ADSGoogle Scholar
  8. [8]
    N.K. Nielsen and P. Olesen, An unstable Yang-Mills field mode, Nucl. Phys. B 144 (1978) 376 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    J. Ambjørn and P. Olesen, On electroweak magnetism, Nucl. Phys. B 315 (1989) 606 [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    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
  11. [11]
    N.S. Manton and N.A. Rink, Vortices on hyperbolic surfaces, J. Phys. A 43 (2010) 434024 [arXiv:0912.2058] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  12. [12]
    P. Sutcliffe, Hyperbolic vortices with large magnetic flux, Phys. Rev. D 85 (2012) 125015 [arXiv:1204.0400] [INSPIRE].ADSGoogle Scholar
  13. [13]
    M. Eto, T. Fujimori, M. Nitta and K. Ohashi, All exact solutions of non-abelian vortices from Yang-Mills instantons, JHEP 07 (2013) 034 [arXiv:1207.5143] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    M.G. Alford, K. Benson, S.R. Coleman, J. March-Russell and F. Wilczek, Zero modes of nonabelian vortices, Nucl. Phys. B 349 (1991) 414 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    M.G. Alford, K. Benson, S.R. Coleman, J. March-Russell and F. Wilczek, The interactions and excitations of nonabelian vortices, Phys. Rev. Lett. 64 (1990) 1632 [Erratum ibid. 65 (1990) 668] [INSPIRE].
  16. [16]
    M.G. Alford, K.-M. Lee, J. March-Russell and J. Preskill, Quantum field theory of nonAbelian strings and vortices, Nucl. Phys. B 384 (1992) 251 [hep-th/9112038] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    H.-K. Lo and J. Preskill, NonAbelian vortices and nonAbelian statistics, Phys. Rev. D 48 (1993) 4821 [hep-th/9306006] [INSPIRE].ADSMathSciNetGoogle Scholar
  18. [18]
    K. Konishi, M. Nitta and W. Vinci, Supersymmetry breaking on gauged non-Abelian vortices, JHEP 09 (2012) 014 [arXiv:1206.4546] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    F. Canfora and G. Tallarita, Constraining monopoles by topology: an autonomous system, JHEP 09 (2014) 136 [arXiv:1407.0609] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    F. Canfora and G. Tallarita, SU(N) BPS monopoles in \( {\mathrm{\mathcal{M}}}^2\times {S}^2 \), arXiv:1502.02957 [INSPIRE].
  21. [21]
    M. Bucher and A. Goldhaber, SO(10) cosmic strings and SU(3)-color Cheshire charge, Phys. Rev. D 49 (1994) 4167 [hep-ph/9310262] [INSPIRE].ADSMathSciNetGoogle Scholar
  22. [22]
    J. Evslin, K. Konishi, M. Nitta, K. Ohashi and W. Vinci, Non-Abelian vortices with an Aharonov-Bohm effect, JHEP 01 (2014) 086 [arXiv:1310.1224] [INSPIRE].ADSCrossRefGoogle Scholar

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© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of Physics “E. Fermi”University of PisaPisaItaly
  2. 2.INFN — Sezione di PisaPisaItaly

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