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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Gerchkovitz and A. Karasik, Vortex-strings in \( \mathcal{N} \) = 2 SQCD and bulk-string decoupling, JHEP 02 (2018) 091 [arXiv:1710.02203] [INSPIRE].
E. Gerchkovitz and A. Karasik, New Vortex-String Worldsheet Theories from Supersymmetric Localization, arXiv:1711.03561 [INSPIRE].
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].
A. Hanany and D. Tong, Vortices, instantons and branes, JHEP 07 (2003) 037 [hep-th/0306150] [INSPIRE].
A. Hanany and D. Tong, Vortex strings and four-dimensional gauge dynamics, JHEP 04 (2004) 066 [hep-th/0403158] [INSPIRE].
M. Shifman and A. Yung, NonAbelian string junctions as confined monopoles, Phys. Rev. D 70 (2004) 045004 [hep-th/0403149] [INSPIRE].
M. Shifman and A. Yung, Non-Abelian semilocal strings in N = 2 supersymmetric QCD, Phys. Rev. D 73 (2006) 125012 [hep-th/0603134] [INSPIRE].
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].
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].
M. Eto et al., Constructing non-Abelian vortices with arbitrary gauge groups, AIP Conf. Proc. 1078 (2009) 483 [INSPIRE].
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].
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].
M. Eto et al., On the moduli space of semilocal strings and lumps, Phys. Rev. D 76 (2007) 105002 [arXiv:0704.2218] [INSPIRE].
M. Eto et al., Non-Abelian Vortices of Higher Winding Numbers, Phys. Rev. D 74 (2006) 065021 [hep-th/0607070] [INSPIRE].
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].
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].
D. Tong, Quantum Vortex Strings: A Review, Annals Phys. 324 (2009) 30 [arXiv:0809.5060] [INSPIRE].
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].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
N. Hama and K. Hosomichi, Seiberg-Witten Theories on Ellipsoids, JHEP 09 (2012) 033 [Addendum ibid. 10 (2012) 051] [arXiv:1206.6359] [INSPIRE].
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].
Y. Pan and W. Peelaers, Ellipsoid partition function from Seiberg-Witten monopoles, JHEP 10 (2015) 183 [arXiv:1508.07329] [INSPIRE].
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].
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].
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].
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].
Y. Pan and W. Peelaers, Intersecting Surface Defects and Instanton Partition Functions, JHEP 07 (2017) 073 [arXiv:1612.04839] [INSPIRE].
D. Tong, Monopoles in the Higgs phase, Phys. Rev. D 69 (2004) 065003 [hep-th/0307302] [INSPIRE].
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].
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].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
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].
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].
D. Gaiotto, L. Rastelli and S.S. Razamat, Bootstrapping the superconformal index with surface defects, JHEP 01 (2013) 022 [arXiv:1207.3577] [INSPIRE].
J. Gomis and B. Le Floch, M2-brane surface operators and gauge theory dualities in Toda, JHEP 04 (2016) 183 [arXiv:1407.1852] [INSPIRE].
J. Gomis and S. Lee, Exact Kähler Potential from Gauge Theory and Mirror Symmetry, JHEP 04 (2013) 019 [arXiv:1210.6022] [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: 1808.00725
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Karasik, A. Vortex-strings in \( \mathcal{N} \) = 2 quiver × U(1) theories. J. High Energ. Phys. 2018, 129 (2018). https://doi.org/10.1007/JHEP12(2018)129
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2018)129