Advertisement

Non-Abelian vortex dynamics: effective world-sheet action

  • Sven Bjarke Gudnason
  • Yunguo Jiang
  • Kenichi Konishi
Article

Abstract

The low-energy vortex effective actionis constructed in a wide class of systems in a color-flavor locked vacuum, which generalizes the results found earlier in the context of U(N) models. It describes the weak fluctuations of the non-Abelian orientational moduli on the vortex worldsheet. For instance, for the minimum vortex in SO(2N) × U(1) or USp(2N) × U(1)gauge theories, the effective action found is a two-dimensional sigma model living on the Hermitian symmetric spaces SO(2N)/U(N) or USp(2N)/U(N), respectively. The fluctuating moduli have the structure of that of a quantum particle state in spinor representations of the GNO dual ofthe color-flavor SO(2N)C+F or USp(2N)C+F symmetry, i.e. of SO(2N) or of SO(2N + 1). Applied to the benchmark U(N) model our procedure reproduces the known \( \mathbb{C}{P^{N - 1}} \) worldsheet action; our recipe allows us to obtain also the effective vortex action for some higher-winding vortices in U(N) and SO(2N) theories.

Keywords

Confinement Solitons Monopoles and Instantons Nonperturbative Effects Sigma Models 

References

  1. [1]
    R. Auzzi, S. Bolognesi, J. Evslin, K. Konishi and A. Yung, Non-Abelian superconductors: vortices and confinement in N = 2 SQCD, Nucl. Phys. B 673 (2003) 187 [hep-th/0307287] [SPIRES]. CrossRefMathSciNetADSGoogle Scholar
  2. [2]
    M. Shifman and A. Yung, Non-Abelian stringjunctions as confined monopoles, Phys. Rev. D 70 (2004) 045004 [hep-th/0403149] [SPIRES].MathSciNetADSGoogle Scholar
  3. [3]
    A. Gorsky, M. Shifman and A. Yung, Non-Abelian Meissner effect in Yang-Mills theories at weak coupling, Phys. Rev. D 71 (2005) 045010 [hep-th/0412082] [SPIRES].ADSGoogle Scholar
  4. [4]
    M. Eto et al., Constructing non-Abelian vortices with arbitrary gauge gr oups, Phys. Lett. B 669 (2008) 98 [arXiv:0802.1020] [SPIRES].MathSciNetADSGoogle Scholar
  5. [5]
    M. Eto et al., Non-Abelian vortices in SO(N) and USp(N) gauge theories, JHEP 06 (2009) 004 [arXiv:0903.4471] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  6. [6]
    L. Ferretti, S.B. Gudnason and K. Konishi, Non-Abelian vortices and monopoles in SO(N) theories, Nucl. Phys. B 789 (2008) 84 [arXiv:0706.3854] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  7. [7]
    F. Delduc and G. Valent, Classical and quantum structure of the compact Kählerian σ-models, Nucl. Phys. B 253 (1985) 494 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  8. [8]
    F. Delduc and G. Valent, Renormalizability of the generalized σ-models defined on compact Hermitian symmetric spaces, Phys. Lett. B 148 (1984) 124 [SPIRES].MathSciNetADSGoogle Scholar
  9. [9]
    A. Hanany and D. Tong, Vortices, instantons and branes, JHEP 07 (2003) 037 [hep-th/0306150] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  10. [10]
    R. Auzzi, S. Bolognesi, J. Evslin and K. Konishi, Non-Abelian monopoles and the vortices that confine them, Nucl. Phys. B 686 (2004) 119 [hep-th/0312233] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  11. [11]
    Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Construction of non-Abelian walls and their complete moduli space, Phys. Rev. Lett. 93 (2004) 161601 [hep-th/0404198] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  12. [12]
    Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, All exact solutions of a 1/4 Bogomol’nyi-Prasad-Sommerfield equation, Phys. Rev. D 71 (2005) 065018 [hep-th/0405129] [SPIRES].MathSciNetADSGoogle Scholar
  13. [13]
    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] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  14. [14]
    M. Eto et al., Fractional vortices and lumps, Phys. Rev. D 80 (2009) 045018 [arXiv:0905.3540] [SPIRES].ADSGoogle Scholar
  15. [15]
    R. Auzzi, M. Eto, S.B. Gudnason, K. Konishi and W. Vinci, On the stability of non-Abelian semi-local vortices, Nucl. Phys. B 813 (2009) 484 [arXiv:0810.5679] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    G. Carlino, K. Konishi and H. Murayama, Dynamical symmetry breaking in supersymmetric SU(n c) and USp(2n c) gauge theories, Nucl. Phys. B 590 (2000) 37 [hep-th/0005076] [SPIRES]. CrossRefMathSciNetADSGoogle Scholar
  17. [17]
    G. Carlino, K. Konishi, S.P. Kumar and H. Murayama, Vacuum structure and flavor symmetry breaking in supersymmetric SO(n c) gauge theories, Nucl. Phys. B 608 (2001) 51 [hep-th/0104064] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    A.Y. Morozov, A.M. Perelomov and M.A. Shifman, Exact Gell-Mann-Low function of supersymmetric Kähler σ-models, Nucl. Phys. B 248 (1984) 279 [SPIRES]. CrossRefMathSciNetADSGoogle Scholar
  19. [19]
    K. Higashijima and M. Nitta, Supersymmetric nonlinear σ-models as gauge theories, Prog. Theor. Phys. 103 (2000) 635 [hep-th/9911139] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  20. [20]
    E. Witten, Constraints on supersymmetry breaking, Nucl. Phys. B 202 (1982) 253 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  21. [21]
    K. Hori and C. Vafa, Mirror symmetry, hep-th/0002222 [SPIRES].
  22. [22]
    C.U. Sánchez, A.L. Calí and J.L. Moreschi, Spheres in Hermitian symmetric spaces and flag manifolds, Geom. Dedicata 64 (1997) 261. MATHCrossRefMathSciNetGoogle Scholar
  23. [23]
    M. Eto et al., Non-Abelian vortices of higher winding numbers, Phys. Rev. D 74 (2006) 065021 [hep-th/0607070] [SPIRES].MathSciNetADSGoogle Scholar
  24. [24]
    M. Eto et al., Non-Abelian duality from vortex moduli: a dual model of color-confinement, Nucl. Phys. B 780 (2007) 161 [hep-th/0611313] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  25. [25]
    R. Auzzi, S. Bolognesi and M. Shifman, Higher winding strings and confined monopoles in N = 2 SQCD, Phys. Rev. D 81 (2010) 085011 [arXiv:1001.1903] [SPIRES].ADSGoogle Scholar
  26. [26]
    M. Eto et al., Group theory of non-Abelian vortices, in preparation.Google Scholar
  27. [27]
    H. Georgi, Lie algebras in particle physics, Advanced Book Program, Westview, U.S.A. (1999).Google Scholar
  28. [28]
    S.B. Gudnason and K. Konishi, Low-energy U(1) × USp(2M) gauge theory from simple high-energy gauge group, Phys. Rev. D 81 (2010) 105007 [arXiv:1002.0850] [SPIRES].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Sven Bjarke Gudnason
    • 1
    • 2
  • Yunguo Jiang
    • 1
    • 2
  • Kenichi Konishi
    • 1
    • 2
  1. 1.Department of PhysicsUniversity of PisaPisaItaly
  2. 2.INFN, Sezione di PisaPisaItaly

Personalised recommendations