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TMF, 2007, Volume 152, Number 3, Pages 476–487 (Mi tmf6104)  

This article is cited in 23 scientific papers (total in 23 papers)

$N=1$ supersymmetric conformal block recursion relations

V. A. Belavinab

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b International School for Advanced Studies (SISSA)

Abstract: We present explicit recursion relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the analytic properties of the superconformal blocks as functions of the conformal dimensions and the central charge of the superconformal algebra. We compare the results with the explicit analytic expressions obtained for special parameter values corresponding to the truncated operator product expansion. These recursion relations are an efficient tool for numerically studying the four-point correlation function in superconformal field theory in the framework of the bootstrap approach, similar to that in the case of the purely conformal symmetry.

Keywords: $N{=}1$ superconformal field theory, four-point conformal block function, recursion relation

DOI: https://doi.org/10.4213/tmf6104

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English version:
Theoretical and Mathematical Physics, 2007, 152:3, 1275–1285

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Received: 01.12.2006

Citation: V. A. Belavin, “$N=1$ supersymmetric conformal block recursion relations”, TMF, 152:3 (2007), 476–487; Theoret. and Math. Phys., 152:3 (2007), 1275–1285

Citation in format AMSBIB
\by V.~A.~Belavin
\paper $N=1$ supersymmetric conformal block recursion relations
\jour TMF
\yr 2007
\vol 152
\issue 3
\pages 476--487
\jour Theoret. and Math. Phys.
\yr 2007
\vol 152
\issue 3
\pages 1275--1285

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    This publication is cited in the following articles:
    1. V. A. Belavin, “Modular integrals in minimal super Liouville gravity”, Theoret. and Math. Phys., 161:1 (2009), 1361–1375  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Belavin A., Belavin V., “Four-point function in super Liouville gravity”, J. Phys. A, 42:30 (2009), 304003, 19 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    3. Suchanek P., “Elliptic recursion for 4-point superconformal blocks and bootstrap in N=1 SLFT”, Journal of High Energy Physics, 2011, no. 2, 090  crossref  mathscinet  zmath  isi  scopus
    4. Belavin V., Feigin B., “Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories”, Journal of High Energy Physics, 2011, no. 7, 079  crossref  mathscinet  zmath  isi  scopus
    5. Osborn H., “Conformal Blocks for Arbitrary Spins in Two Dimensions”, Phys. Lett. B, 718:1 (2012), 169–172  crossref  mathscinet  adsnasa  isi  elib  scopus
    6. Belavin V., “Conformal Blocks of Chiral Fields in N=2 Susy CFT and Affine Laumon Spaces”, J. High Energy Phys., 2012, no. 10, 156  crossref  mathscinet  isi  elib  scopus
    7. Hadasz L., Jaskolski Z., Suchanek P., “Recurrence Relations for Toric N=1 Superconformal Blocks”, J. High Energy Phys., 2012, no. 9, 122  crossref  mathscinet  isi  scopus
    8. Belavin A., Mukhametzhanov B., “N=1 Superconformal Blocks with Ramond Fields From AGT Correspondence”, J. High Energy Phys., 2013, no. 1, 178  crossref  mathscinet  zmath  isi  elib  scopus
    9. Fitzpatrick A.L., Kaplan J., Khandker Z.U., Li D., Poland D., Simmons-Duffin D., “Covariant Approaches To Superconformal Blocks”, J. High Energy Phys., 2014, no. 8, 129  crossref  isi  scopus
    10. Ahn Ch., Stanishkov M., “On the Renormalization Group Flow in Two Dimensional Superconformal Models”, Nucl. Phys. B, 885 (2014), 713–733  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Bershtein M.A., Shchechkin A.I., “Bilinear Equations on Painlevé Tau Functions From CFT”, Commun. Math. Phys., 339:3 (2015), 1021–1061  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Beccaria M., Fachechi A., Macorini G., Martina L., “Exact partition functions for deformed N = 2
      $$ \mathcal{N}=2 $$
      theories with N f = 4
      $$ {\mathcal{N}}_f=4 $$
      flavours”, J. High Energy Phys., 2016, no. 12, 029  crossref  mathscinet  isi  elib  scopus
    13. Ciosmak P., Hadasz L., Manabe M., Sulkowski P., “Super-quantum curves from super-eigenvalue models”, J. High Energy Phys., 2016, no. 10, 044  crossref  mathscinet  isi  elib  scopus
    14. Chen H., Fitpatrick A.L., Kaplan J., Li D., Wang J., “Degenerate operators and the 1/c expansion: Lorentzian resummations, high order computations, and super-Virasoro blocks”, J. High Energy Phys., 2017, no. 3, 167  crossref  mathscinet  isi  scopus
    15. Bershtein M.A., Shchechkin A.I., “Bäcklund transformation of Painlevé III( D _{8} ) \textit function”, J. Phys. A-Math. Theor., 50:11 (2017), 115205  crossref  mathscinet  zmath  isi  scopus
    16. Poghosyan H., “The Light Asymptotic Limit of Conformal Blocks in N=1 Super Liouville Field Theory”, J. High Energy Phys., 2017, no. 9, 062  crossref  mathscinet  isi  scopus
    17. Poghossian R., “Recurrence Relations For the W-3 Conformal Blocks and N=2 SYM Partition Functions”, J. High Energy Phys., 2017, no. 11, 053  crossref  mathscinet  isi  scopus
    18. Lin Y.-H., Shao Sh.-H., Wang Y., Yin X., “(2,2) Superconformal Bootstrap in Two Dimensions”, J. High Energy Phys., 2017, no. 5, 112  crossref  mathscinet  isi  scopus
    19. Belavina V., Geiko R., “C-Recursion For Multi-Point Superconformal Blocks. Ns Sector”, J. High Energy Phys., 2018, no. 8, 112  crossref  isi  scopus
    20. Hikida Ya., Uetoko T., “Superconformal Blocks From Wilson Lines With Loop Corrections”, J. High Energy Phys., 2018, no. 8, 101  crossref  mathscinet  zmath  isi  scopus
    21. Lodato I., Merbis W., Zodinmawia, “Supersymmetric Galilean Conformal Blocks”, J. High Energy Phys., 2018, no. 9, 086  crossref  mathscinet  isi  scopus
    22. Kos F., Oh J., “2D Small N=4 Long-Multiplet Superconformal Block”, J. High Energy Phys., 2019, no. 2, 001  crossref  isi  scopus
    23. Belavin V., Zhakenov A., “Agt Basis in Scft For C=3/2 and Uglov Polynomials”, Nucl. Phys. B, 958 (2020), 115133  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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