Skip to main content
SpringerLink
Log in

SUSY gauge theories on squashed three-spheres

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We study Euclidean 3D \( \mathcal{N} = 2 \) supersymmetric gauge theories on squashed three-spheres preserving isometries SU(2) × U(1) or U(1) × U(1). We show that, when a suitable background U(1) gauge field is turned on, these squashed spheres support charged Killing spinors and therefore \( \mathcal{N} = 2 \) supersymmetric gauge theories. We present the Lagrangian and supersymmetry rules for general gauge theories. The partition functions are computed using localization principle, and are expressed as integrals over Coulomb branch. For the squashed sphere with U(1) × U(1) isometry, its measure and integrand are identified with the building blocks of structure constants in Liouville or Toda conformal field theories with b ≠ 1.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  2. A. Kapustin, B. Willett and I. Yaakov, Nonperturbative Tests of Three-Dimensional Dualities, JHEP 10 (2010) 013 [arXiv:1003.5694] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, arXiv:1012.3210 [SPIRES].

  4. N. Hama, K. Hosomichi and S. Lee, Notes on SUSY Gauge Theories on Three-Sphere, JHEP 03 (2011) 127 [arXiv:1012.3512] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  5. T. Suyama, On Large-N Solution of ABJM Theory, Nucl. Phys. B 834 (2010) 50 [arXiv:0912.1084] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. S.-J. Rey and T. Suyama, Exact Results and Holography of Wilson Loops in N = 2 Superconformal (Quiver) Gauge Theories, JHEP 01 (2011) 136 [arXiv:1001.0016] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. M. Mariño, S. Pasquetti and P. Putrov, Large-N duality beyond the genus expansion, JHEP 07 (2010) 074 [arXiv:0911.4692] [SPIRES].

    Article  ADS  Google Scholar 

  8. N. Drukker and D. Trancanelli, A supermatrix model for N = 6 super Chern-Simons-matter theory, JHEP 02 (2010) 058 [arXiv:0912.3006] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. M. Mariño and P. Putrov, Exact Results in ABJM Theory from Topological Strings, JHEP 06 (2010) 011 [arXiv:0912.3074] [SPIRES].

    Article  ADS  Google Scholar 

  10. N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, arXiv:1007.3837 [SPIRES].

  11. S. Kim, The complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [arXiv:0903.4172] [SPIRES].

    Article  ADS  Google Scholar 

  12. Y. Imamura and S. Yokoyama, Index for three dimensional superconformal field theories with general R-charge assignments, JHEP 04 (2011) 007 [arXiv:1101.0557] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  13. Y. Imamura, D. Yokoyama and S. Yokoyama, Superconformal index for large-N quiver Chern-Simons theories, arXiv:1102.0621 [SPIRES].

  14. S. Cheon, D. Gang, S. Kim and J. Park, Refined test of AdS4/CFT3 correspondence for N = 2,3 theories, arXiv:1102.4273 [SPIRES].

  15. V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, arXiv:0712.2824 [SPIRES].

  16. L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. N. Wyllard, A N−1 conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories, JHEP 11 (2009) 002 [arXiv:0907.2189] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. N. Drukker, D. Gaiotto and J. Gomis, The Virtue of Defects in 4D Gauge Theories and 2D CFTs, arXiv:1003.1112 [SPIRES].

  19. K. Hosomichi, S. Lee and J. Park, AGT on the S-duality Wall, JHEP 12 (2010) 079 [arXiv:1009.0340] [SPIRES].

    Article  ADS  Google Scholar 

  20. S. Kharchev, D. Lebedev and M. Semenov-Tian-Shansky, Unitary representations of U q (sl(2,R)), the modular double and the multiparticle q-deformed Toda chains, Commun. Math. Phys. 225 (2002) 573 [hep-th/0102180] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. A.G. Bytsko and J. Teschner, Quantization of models with non-compact quantum group symmetry: Modular XXZ magnet and lattice sinh-Gordon model, J. Phys. A 39 (2006) 12927 [hep-th/0602093] [SPIRES].

    MathSciNet  Google Scholar 

  22. N. Nekrasov and E. Witten, The Omega Deformation, Branes, Integrability and Liouville Theory, JHEP 09 (2010) 092 [arXiv:1002.0888] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan

    Naofumi Hama & Kazuo Hosomichi

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, U.K.

    Sungjay Lee

Authors
  1. Naofumi Hama
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kazuo Hosomichi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sungjay Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kazuo Hosomichi.

Additional information

ArXiv ePrint: 1102.4716

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hama, N., Hosomichi, K. & Lee, S. SUSY gauge theories on squashed three-spheres. J. High Energ. Phys. 2011, 14 (2011). https://doi.org/10.1007/JHEP05(2011)014

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2011)014

Keywords

Search

Navigation