Abstract
We study Virasoro minimal-model 4-point conformal blocks on the sphere and 0-point conformal blocks on the torus (the Virasoro characters), as solutions of Zamolodchikov-type recursion relations. In particular, we study the singularities due to resonances of the dimensions of conformal fields in minimal-model representations, that appear in the intermediate steps of solving the recursion relations, but cancel in the final results.
Article PDF
Similar content being viewed by others
References
V. Belavin, X. Cao, B. Estienne and R. Santachiara, Second level semi-degenerate fields in \( {\mathcal{W}}_3 \) Toda theory: matrix element and differential equation, JHEP 03 (2017) 008 [arXiv:1610.07993] [INSPIRE].
V. Belavin, B. Estienne, O. Foda and R. Santachiara, Correlation functions with fusion-channel multiplicity in \( {\mathcal{W}}_3 \) Toda field theory, JHEP 06 (2016) 137 [arXiv:1602.03870] [INSPIRE].
V.A. Fateev and A.V. Litvinov, On AGT conjecture, JHEP 02 (2010) 014 [arXiv:0912.0504] [INSPIRE].
B.L. Feigin and D.B. Fuks, Invariant skew-symmetric differential operators on the line and Verma modules over the Virasoro algebra, Funct. Anal. Appl. 16 (1982) 114.
B.L. Feigin and D.B. Fuks, Verma modules over the Virasoro algebra, Funct. Anal. Appl. 17 (1982) 241.
L. Hadasz, Z. Jaskolski and P. Suchanek, Recursive representation of the torus 1-point conformal block, JHEP 01 (2010) 063 [arXiv:0911.2353] [INSPIRE].
E. Perlmutter, Virasoro conformal blocks in closed form, JHEP 08 (2015) 088 [arXiv:1502.07742] [INSPIRE].
M. Picco, S. Ribault and R. Santachiara, A conformal bootstrap approach to critical percolation, SciPost 1 (2016) 009.
M. Picco, S. Ribault and R. Santachiara, A conformal bootstrap solution for critical Potts clusters, in progress.
R. Poghossian, Recursion relations in CFT and N = 2 SYM theory, JHEP 12 (2009) 038 [arXiv:0909.3412] [INSPIRE].
R. Poghossian, Recurrence relations for the \( {\mathcal{W}}_3 \) conformal blocks and \( \mathcal{N}=2 \) SYM partition functions, JHEP 11 (2017) 053 [Erratum ibid. 01 (2018) 088] [arXiv:1705.00629] [INSPIRE].
S. Ribault and R. Santachiara, Liouville theory with a central charge less than one, JHEP 08 (2015) 109.
S. Ribault, Conformal field theory on the plane, arXiv:1406.4290 [INSPIRE].
Al.B. Zamolodchikov, Conformal symmetry in two dimensions: an explicit recurrence formula for the conformal partial wave amplitude, Commun. Math. Phys. 96 (1984) 419.
Al.B. Zamolodchikov, Conformal symmetry in two-dimensional space: recursion representation of conformal block, Theor. Math. Phys. 73 (1987) 1088.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1806.02790
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Javerzat, N., Santachiara, R. & Foda, O. Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models. J. High Energ. Phys. 2018, 183 (2018). https://doi.org/10.1007/JHEP08(2018)183
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2018)183