Skip to main content
Log in

N = 1 superconformal blocks with Ramond fields from AGT correspondence

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

Abstract

We use AGT correspondence between N = 2 SUSY Yang-Mills theory on \( {{\mathbb{R}}^4}/{{\mathbb{Z}}_2} \) and two-dimensional CFT model with the algebra \( \mathcal{H} \)\( \widehat{s}l \) (2)2 ⨁ NSR to obtain the explicit expressions for 4-point NSR conformal blocks including Ramond fields in terms of Nekrasov partition functions and correlation functions of \( \widehat{s}l \) (2)2 WZW model.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. 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] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. A. Mironov and A. Morozov, On AGT relation in the case of U(3), Nucl. Phys. B 825 (2010) 1 [arXiv:0908.2569] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. L.F. Alday and Y. Tachikawa, Affine SL(2) conformal blocks from 4d gauge theories, Lett. Math. Phys. 94 (2010) 87 [arXiv:1005.4469] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. V. Belavin and B. Feigin, Super Liouville conformal blocks from N = 2 SU(2) quiver gauge theories, JHEP 07 (2011) 079 [arXiv:1105.5800] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. A. Belavin, V. Belavin and M. Bershtein, Instantons and 2d superconformal field theory, JHEP 09 (2011) 117 [arXiv:1106.4001] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. G. Bonelli, K. Maruyoshi and A. Tanzini, Instantons on ALE spaces and super Liouville conformal field theories, JHEP 08 (2011) 056 [arXiv:1106.2505] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. G. Bonelli, K. Maruyoshi and A. Tanzini, Gauge theories on ALE space and super Liouville correlation functions, Lett. Math. Phys. 101 (2012) 103 [arXiv:1107.4609] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. N. Wyllard, Coset conformal blocks and N = 2 gauge theories, arXiv:1109.4264 [INSPIRE].

  10. M. Alfimov and G. Tarnopolsky, Parafermionic Liouville field theory and instantons on ALE spaces, JHEP 02 (2012) 036 [arXiv:1110.5628] [INSPIRE].

    Article  ADS  Google Scholar 

  11. V. Belavin and N. Wyllard, N = 2 superconformal blocks and instanton partition functions, JHEP 06 (2012) 173 [arXiv:1205.3091] [INSPIRE].

    Article  ADS  Google Scholar 

  12. V. Belavin, Conformal blocks of Chiral fields in N = 2 SUSY CFT and Affine Laumon Spaces, JHEP 10 (2012) 156 [arXiv:1209.2992] [INSPIRE].

    Article  ADS  Google Scholar 

  13. Y. Ito, Ramond sector of super Liouville theory from instantons on an ALE space, Nucl. Phys. B 861 (2012) 387 [arXiv:1110.2176] [INSPIRE].

    Article  ADS  Google Scholar 

  14. N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [INSPIRE].

    MathSciNet  Google Scholar 

  15. H. Nakajima, Heisenberg algebra and Hilbert schemes of points on projective surfaces, Ann. Math. 145 (1997) 379 [alg-geom/9507012].

    Article  MathSciNet  MATH  Google Scholar 

  16. H. Nakajima, Quiver varieties and Kac-Moody algebras, Duke Math. 91 (1998) 515.

    Article  MathSciNet  MATH  Google Scholar 

  17. M. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984) 1 [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  18. V.A. Alba, V.A. Fateev, A.V. Litvinov and G.M. Tarnopolskiy, On combinatorial expansion of the conformal blocks arising from AGT conjecture, Lett. Math. Phys. 98 (2011) 33 [arXiv:1012.1312] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. F. Fucito, J.F. Morales and R. Poghossian, Multi instanton calculus on ALE spaces, Nucl. Phys. B 703 (2004) 518 [hep-th/0406243] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. A. Belavin, M. Bershtein, B. Feigin, A. Litvinov and G. Tarnopolsky, Instanton moduli spaces and bases in coset conformal field theory, arXiv:1111.2803 [INSPIRE].

  21. U. Bruzzo, R. Poghossian and A. Tanzini, Poincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces, Commun. Math. Phys. 304 (2011) 395 [arXiv:0909.1458] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. V. Kac, Infinite-dimensional Lie Algebras, Cambridge University Press, Cambridge U.K. (1995).

    Google Scholar 

  23. P. Goddard, A. Kent and D.I. Olive, Unitary representations of the Virasoro and supervirasoro algebras, Commun. Math. Phys. 103 (1986) 105 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. V. Fateev and A. Zamolodchikov, Parafermionic Currents in the Two-Dimensional Conformal Quantum Field Theory and Selfdual Critical Points in Z(n) Invariant Statistical Systems, Sov. Phys. JETP 62 (1985) 215 [INSPIRE].

    MathSciNet  Google Scholar 

  25. A. Belavin, A.M. Polyakov and A. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. V. Belavin, N = 1 supersymmetric conformal block recursion relations, Theor. Math. Phys. 152 (2007) 1275 [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  27. L. Hadasz, Z. Jaskolski and P. Suchanek, Recursion representation of the Neveu-Schwarz superconformal block, JHEP 03 (2007) 032 [hep-th/0611266] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. L. Hadasz, Z. Jaskolski and P. Suchanek, Elliptic recurrence representation of the N = 1 superconformal blocks in the Ramond sector, JHEP 11 (2008) 060 [arXiv:0810.1203] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. P. Suchanek, Elliptic recursion for 4-point superconformal blocks and bootstrap in N = 1 SLFT, JHEP 02 (2011) 090 [arXiv:1012.2974] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. E. Carlsson and A. Okounkov, Exts and Vertex Operators, arXiv:0801.2565.

  31. V. Schomerus and P. Suchanek, Liouvilles Imaginary Shadow, arXiv:1210.1856 [INSPIRE].

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Baur Mukhametzhanov.

Additional information

ArXiv ePrint: 1210.7454

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belavin, A., Mukhametzhanov, B. N = 1 superconformal blocks with Ramond fields from AGT correspondence. J. High Energ. Phys. 2013, 178 (2013). https://doi.org/10.1007/JHEP01(2013)178

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP01(2013)178

Keywords

Navigation