General Omega deformations from closed string backgrounds

  • Susanne Reffert


In this note, an important extension to the recent construction of the fluxtrap background is presented. The fluxtrap is a closed string background based on the Melvin solution corresponding to the Omega deformation of flat space. In this note, we introduce the mechanisms to extend it from ε 1 = −ε 2\( \mathbb{R} \) to more general values of ε 1 and ε 2 in \( \mathbb{C} \).


Brane Dynamics in Gauge Theories D-branes 


  1. [1]
    G.W. Moore, N. Nekrasov and S. Shatashvili, Integrating over Higgs branches, Commun. Math. Phys. 209 (2000) 97 [hep-th/9712241] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  2. [2]
    A. Lossev, N. Nekrasov and S.L. Shatashvili, Testing Seiberg-Witten solution, hep-th/9801061 [INSPIRE].
  3. [3]
    N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [INSPIRE].MathSciNetGoogle Scholar
  4. [4]
    N.A. Nekrasov and S.L. Shatashvili, Quantization of integrable systems and four dimensional gauge theories, arXiv:0908.4052 [INSPIRE].
  5. [5]
    N. Nekrasov and E. Witten, The Ω deformation, branes, integrability and Liouville theory, JHEP 09 (2010) 092 [arXiv:1002.0888] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    T.J. Hollowood, A. Iqbal and C. Vafa, Matrix models, geometric engineering and elliptic genera, JHEP 03 (2008) 069 [hep-th/0310272] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    A. Iqbal, C. Kozcaz and C. Vafa, The refined topological vertex, JHEP 10 (2009) 069 [hep-th/0701156] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    I. Antoniadis, S. Hohenegger, K. Narain and T. Taylor, Deformed topological partition function and Nekrasov backgrounds, Nucl. Phys. B 838 (2010) 253 [arXiv:1003.2832] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    D. Krefl and J. Walcher, Extended holomorphic anomaly in gauge theory, Lett. Math. Phys. 95 (2011) 67 [arXiv:1007.0263] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  10. [10]
    M.-X. Huang and A. Klemm, Direct integration for general Ω backgrounds, arXiv:1009.1126 [INSPIRE].
  11. [11]
    M. Aganagic, M.C. Cheng, R. Dijkgraaf, D. Krefl and C. Vafa, Quantum geometry of refined topological strings, arXiv:1105.0630 [INSPIRE].
  12. [12]
    S. Hellerman, D. Orlando and S. Reffert, String theory of the Ω deformation, JHEP 01 (2012) 148 [arXiv:1106.0279] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    D. Orlando and S. Reffert, Relating gauge theories via gauge/Bethe correspondence, JHEP 10 (2010) 071 [arXiv:1005.4445] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    D. Orlando and S. Reffert, The gauge-Bethe correspondence and geometric representation theory, Lett. Math. Phys. 98 (2011) 289 [arXiv:1011.6120] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  15. [15]
    N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, hep-th/0306238 [INSPIRE].
  16. [16]
    J. Russo and A.A. Tseytlin, Supersymmetric fluxbrane intersections and closed string tachyons, JHEP 11 (2001) 065 [hep-th/0110107] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Institute for the Physics and Mathematics of the UniverseUniversity of TokyoKashiwa-shiJapan

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