N=1 SUSY Conformal Block Recursive Relations

Abstract

We present explicit recursive 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. The results are compared with the explicit analytic expressions obtained for special parameter values corresponding to the truncated operator product expansion. These recursive relations are an efficient tool for numerically studying the four-point correlation function in Super Conformal Field Theory in the framework of the bootstrap approach, similar to that in the case of the purely conformal symmetry.

12 pages, typos corrected, reference added

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• Two and three-point functions in Liouville theory
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• Four-point function in Super Liouville Gravity
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• The light asymptotic limit of conformal blocks in $\mathcal{N}=1$ super Liouville field theory
• Modular Integrals in Minimal Super Liouville Gravity
• AGT basis in SCFT for c=3/2 and Uglov Polynomials