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Exact results for supersymmetric abelian vortex loops in 2 + 1 dimensions

  • Anton Kapustin
  • Brian Willett
  • Itamar Yaakov
Article

Abstract

We define a class of supersymmetric defect loop operators in \( \mathcal{N} \) = 2 gauge theories in 2 + 1 dimensions. We give a prescription for computing the expectation value of such operators in a generic \( \mathcal{N} \) = 2 theory on the three-sphere using localization. We elucidate the role of defect loop operators in IR dualities of supersymmetric gauge theories, and write down their transformation properties under the SL(2, \( \mathbb{Z} \)) action on conformal theories with abelian global symmetries.

Keywords

Supersymmetric gauge theory Duality in Gauge Field Theories Solitons Monopoles and Instantons 

References

  1. [1]
    G. Hooft, On the Phase Transition Towards Permanent Quark Confinement, Nucl. Phys. B 138 (1978) 1 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    C. Montonen and D.I. Olive, Magnetic Monopoles as Gauge Particles?, Phys. Lett. B 72 (1977) 117 [INSPIRE].ADSGoogle Scholar
  3. [3]
    E. Witten and D.I. Olive, Supersymmetry Algebras That Include Topological Charges, Phys. Lett. B 78 (1978) 97 [INSPIRE].ADSGoogle Scholar
  4. [4]
    A. Kapustin, Wilson-t Hooft operators in four-dimensional gauge theories and S-duality, Phys. Rev. D 74 (2006) 025005 [hep-th/0501015] [INSPIRE].MathSciNetADSGoogle Scholar
  5. [5]
    N. Drukker, J. Gomis and D. Young, Vortex Loop Operators, M2-branes and Holography, JHEP 03 (2009) 004 [arXiv:0810.4344] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    S. Gukov and E. Witten, Gauge Theory, Ramification, And The Geometric Langlands Program, hep-th/0612073 [INSPIRE].
  7. [7]
    G.W. Moore and N. Seiberg, Taming the Conformal Zoo, Phys. Lett. B 220 (1989) 422 [INSPIRE].MathSciNetADSGoogle Scholar
  8. [8]
    E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351.MathSciNetADSMATHCrossRefGoogle Scholar
  9. [9]
    V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  10. [10]
    M. Blau and G. Thompson, Localization and diagonalization: A review of functional integral techniques for low dimensional gauge theories and topological field theories, J. Math. Phys. 36 (1995) 2192 [hep-th/9501075] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  11. [11]
    E. Witten, Topological Quantum Field Theory, Commun. Math. Phys. 117 (1988) 353.MathSciNetADSMATHCrossRefGoogle Scholar
  12. [12]
    J. Gomis, T. Okuda and V. Pestun, Exact Results fort Hooft Loops in Gauge Theories on S4, JHEP 05 (2012) 141 [arXiv:1105.2568] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    M. Mariño, Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories, J. Phys. A 44 (2011) 463001 [arXiv:1104.0783] [INSPIRE].ADSGoogle Scholar
  15. [15]
    E. Witten, SL(2, \( \mathbb{Z} \)) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [INSPIRE].
  16. [16]
    D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    T. Dimofte, D. Gaiotto and S. Gukov, Gauge Theories Labelled by Three-Manifolds, arXiv:1108.4389 [INSPIRE].
  18. [18]
    T. Dimofte, D. Gaiotto and S. Gukov, 3-Manifolds and 3d Indices, arXiv:1112.5179 [INSPIRE].
  19. [19]
    O. Aharony, IR duality in D = 3 N = 2 supersymmetric USp(2N(c)) and U(N(c)) gauge theories, Phys. Lett. B 404 (1997) 71 [hep-th/9703215] [INSPIRE].MathSciNetADSGoogle Scholar
  20. [20]
    A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Department of PhysicsCalifornia Institute of TechnologyPasadenaU.S.A
  2. 2.Institute for Advanced StudyPrincetonU.S.A
  3. 3.Department of PhysicsPrinceton UniverityPrincetonU.S.A

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