Thanks to visit codestin.com
Credit goes to link.springer.com

Skip to main content
Springer Nature Link
Log in

Recursive representation of the torus 1-point conformal block

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

Abstract

The recursive relation for the 1-point conformal block on a torus is derived and used to prove the identities between conformal blocks recently conjectured by Poghossian in [1]. As an illustration of the efficiency of the recurrence method the modular invariance of the 1-point Liouville correlation function is numerically analyzed.

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

Access this article

Log in via an institution

Subscribe and save

Springer+
from £29.99 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.

References

  1. R. Poghossian, Recursion relations in CFT and N = 2 SYM theory, JHEP 12 (2009) 038 [arXiv:0909.3412] [SPIRES].

    Article  Google Scholar 

  2. L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from four-dimensional gauge theories, arXiv:0906.3219 [SPIRES].

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

    Article  Google Scholar 

  4. A. Marshakov, A. Mironov and A. Morozov, On combinatorial expansions of conformal blocks, arXiv:0907.3946 [SPIRES].

  5. D. Gaiotto, Asymptotically free N = 2 theories and irregular conformal blocks, arXiv:0908.0307 [SPIRES].

  6. A. Mironov, S. Mironov, A. Morozov and A. Morozov, CFT exercises for the needs of AGT, arXiv:0908.2064 [SPIRES].

  7. L.F. Alday, D. Gaiotto, S. Gukov, Y. Tachikawa and H. Verlinde, Loop and surface operators in N = 2 gauge theory and Liouville modular geometry, arXiv:0909.0945 [SPIRES].

  8. A. Marshakov, A. Mironov and A. Morozov, Zamolodchikov asymptotic formula and instanton expansion in N = 2 SUSY N f = 2N c QCD, JHEP 11 (2009) 048 [arXiv:0909.3338] [SPIRES].

    Article  Google Scholar 

  9. A. Mironov and A. Morozov, Proving AGT relations in the large-c limit, Phys. Lett. B 682 (2009) 118 [arXiv:0909.3531] [SPIRES].

    Google Scholar 

  10. G. Bonelli and A. Tanzini, Hitchin systems, N = 2 gauge theories and W-gravity, arXiv:0909.4031 [SPIRES].

  11. V. Alba and A. Morozov, Non-conformal limit of AGT relation from the 1-point torus conformal block, arXiv:0911.0363 [SPIRES].

  12. A.B. Zamolodchikov, Conformal symmetry in two-dimensions: an explicit recurrence formula for the conformal partial wave amplitude, Commun. Math. Phys. 96 (1984) 419 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. Al. Zamolodchikov, Two-dimensional conformal symmetry and critical four-spin correlation functions in the Ashkin-Teller model, Sov. Phys. JETP 63 (1986) 1061.

    MathSciNet  Google Scholar 

  14. Al. Zamolodchikov, Conformal symmetry in two-dimensional space: recursion representation of conformal block, Theor. Math. Phys. 73 (1987) 1088.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  16. V.A. Fateev, A.V. Litvinov, A. Neveu and E. Onofri, Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks, J. Phys. A 42 (2009) 304011 [arXiv:0902.1331] [SPIRES].

    MathSciNet  Google Scholar 

  17. A. Zamolodchikov, Higher equations of motion in Liouville field theory, Int. J. Mod. Phys. A 19S2 (2004) 510 [hep-th/0312279] [SPIRES].

    MathSciNet  Google Scholar 

  18. H. Sonoda, Sewing conformal field theories. 2, Nucl. Phys. B 311 (1988) 417 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. A.B. Zamolodchikov and A.B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory, Nucl. Phys. B 477 (1996) 577 [hep-th/9506136] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059, Kraków, Poland

    Leszek Hadasz

  2. Institute of Theoretical Physics, University of Wrocław, pl. M. Borna, 50-204, Wrocław, Poland

    Zbigniew Jaskólski & Paulina Suchanek

Authors
  1. Leszek Hadasz
    View author publications

    Search author on:PubMed Google Scholar

  2. Zbigniew Jaskólski
    View author publications

    Search author on:PubMed Google Scholar

  3. Paulina Suchanek
    View author publications

    Search author on:PubMed Google Scholar

Corresponding author

Correspondence to Leszek Hadasz.

Additional information

ArXiv ePrint: 0911.2353

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hadasz, L., Jaskólski, Z. & Suchanek, P. Recursive representation of the torus 1-point conformal block. J. High Energ. Phys. 2010, 63 (2010). https://doi.org/10.1007/JHEP01(2010)063

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP01(2010)063

Keywords