Advertisement

Journal of High Energy Physics

, 2018:129 | Cite as

Vortex-strings in \( \mathcal{N} \) = 2 quiver × U(1) theories

  • Avner KarasikEmail author
Open Access
Regular Article - Theoretical Physics
  • 33 Downloads

Abstract

We study \( \frac{1}{2} \)-BPS vortex-strings in four dimensional \( \mathcal{N} \) = 2 supersymmetric quiver theories with gauge group SU(N)n × U(1). The matter content of the quiver can be represented by what we call a tetris diagram, which simplifies the analysis of the Higgs vacua and the corresponding strings. We classify the vacua of these theories in the presence of a Fayet-Iliopoulos term, and study strings above fully-Higgsed vacua. The strings are studied using classical zero modes analysis, supersymmetric localization and, in some cases, also S-duality. We analyze the conditions for bulk-string decoupling at low energies. When the conditions are satisfied, the low energy theory living on the string’s worldsheet is some 2d \( \mathcal{N} \) = (2, 2) supersymmetric non-linear sigma model. We analyze the conditions for weak→weak 2d-4d map of parameters, and identify the worldsheet theory in all the cases where the map is weak→weak. For some SU(2) quivers, S-duality can be used to map weakly coupled worldsheet theories to strongly coupled ones. In these cases, we are able to identify the worldsheet theories also when the 2d-4d map of parameters is weak→strong.

Keywords

Sigma Models Supersymmetric Gauge Theory Solitons Monopoles and Instantons Supersymmetry and Duality 

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]
    E. Gerchkovitz and A. Karasik, Vortex-strings in \( \mathcal{N} \) = 2 SQCD and bulk-string decoupling, JHEP 02 (2018) 091 [arXiv:1710.02203] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    E. Gerchkovitz and A. Karasik, New Vortex-String Worldsheet Theories from Supersymmetric Localization, arXiv:1711.03561 [INSPIRE].
  3. [3]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    A. Hanany and D. Tong, Vortices, instantons and branes, JHEP 07 (2003) 037 [hep-th/0306150] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    A. Hanany and D. Tong, Vortex strings and four-dimensional gauge dynamics, JHEP 04 (2004) 066 [hep-th/0403158] [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. 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
  8. [8]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    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].
  10. [10]
    M. Eto et al., Constructing non-Abelian vortices with arbitrary gauge groups, AIP Conf. Proc. 1078 (2009) 483 [INSPIRE].ADSGoogle Scholar
  11. [11]
    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] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    N. Dorey, T.J. Hollowood and D. Tong, The BPS spectra of gauge theories in two-dimensions and four-dimensions, JHEP 05 (1999) 006 [hep-th/9902134] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    M. Eto et al., On the moduli space of semilocal strings and lumps, Phys. Rev. D 76 (2007) 105002 [arXiv:0704.2218] [INSPIRE].ADSMathSciNetGoogle Scholar
  14. [14]
    M. Eto et al., Non-Abelian Vortices of Higher Winding Numbers, Phys. Rev. D 74 (2006) 065021 [hep-th/0607070] [INSPIRE].ADSMathSciNetGoogle Scholar
  15. [15]
    M. Shifman and A. Yung, Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories, Rev. Mod. Phys. 79 (2007) 1139 [hep-th/0703267] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  16. [16]
    D. Tong, TASI lectures on solitons: Instantons, monopoles, vortices and kinks, in Theoretical Advanced Study Institute in Elementary Particle Physics: Many Dimensions of String Theory (TASI 2005), Boulder, Colorado, June 5–July 1, 2005 (2005) hep-th/0509216 [INSPIRE].
  17. [17]
    D. Tong, Quantum Vortex Strings: A Review, Annals Phys. 324 (2009) 30 [arXiv:0809.5060] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    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].ADSMathSciNetzbMATHGoogle Scholar
  19. [19]
    V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    N. Hama and K. Hosomichi, Seiberg-Witten Theories on Ellipsoids, JHEP 09 (2012) 033 [Addendum ibid. 10 (2012) 051] [arXiv:1206.6359] [INSPIRE].
  21. [21]
    H.-Y. Chen and T.-H. Tsai, On Higgs branch localization of Seiberg-Witten theories on an ellipsoid, PTEP 2016 (2016) 013B09 [arXiv:1506.04390] [INSPIRE].
  22. [22]
    Y. Pan and W. Peelaers, Ellipsoid partition function from Seiberg-Witten monopoles, JHEP 10 (2015) 183 [arXiv:1508.07329] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    T. Fujimori, T. Kimura, M. Nitta and K. Ohashi, 2d partition function in Ω-background and vortex/instanton correspondence, JHEP 12 (2015) 110 [arXiv:1509.08630] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  24. [24]
    N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact Results in D = 2 Supersymmetric Gauge Theories, JHEP 05 (2013) 093 [arXiv:1206.2606] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    F. Benini and S. Cremonesi, Partition Functions of \( \mathcal{N} \) = (2, 2) Gauge Theories on S 2 and Vortices, Commun. Math. Phys. 334 (2015) 1483 [arXiv:1206.2356] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  26. [26]
    J. Gomis, B. Le Floch, Y. Pan and W. Peelaers, Intersecting Surface Defects and Two-Dimensional CFT, Phys. Rev. D 96 (2017) 045003 [arXiv:1610.03501] [INSPIRE].ADSMathSciNetGoogle Scholar
  27. [27]
    Y. Pan and W. Peelaers, Intersecting Surface Defects and Instanton Partition Functions, JHEP 07 (2017) 073 [arXiv:1612.04839] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    D. Tong, Monopoles in the Higgs phase, Phys. Rev. D 69 (2004) 065003 [hep-th/0307302] [INSPIRE].ADSGoogle Scholar
  29. [29]
    N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    P.C. Argyres and A. Buchel, New S dualities in N = 2 supersymmetric SU(2) × SU(2) gauge theory, JHEP 11 (1999) 014 [hep-th/9910125] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    Y. Tachikawa, N = 2 supersymmetric dynamics for pedestrians, vol. 890 (2014) DOI: https://doi.org/10.1007/978-3-319-08822-8 [arXiv:1312.2684] [INSPIRE].
  33. [33]
    N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    D. Gaiotto, L. Rastelli and S.S. Razamat, Bootstrapping the superconformal index with surface defects, JHEP 01 (2013) 022 [arXiv:1207.3577] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    J. Gomis and B. Le Floch, M2-brane surface operators and gauge theory dualities in Toda, JHEP 04 (2016) 183 [arXiv:1407.1852] [INSPIRE].ADSzbMATHGoogle Scholar
  36. [36]
    J. Gomis and S. Lee, Exact Kähler Potential from Gauge Theory and Mirror Symmetry, JHEP 04 (2013) 019 [arXiv:1210.6022] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Particle Physics and AstrophysicsWeizmann Institute of ScienceRehovotIsrael

Personalised recommendations