Elliptic recursion for 4-point superconformal blocks and bootstrap in N=1 SLFT

TL;DR

This paper introduces and analyzes all types of 4-point superconformal blocks in N=1 superconformal field theory, deriving elliptic recurrence relations and numerically verifying crossing symmetry in super Liouville theory.

Contribution

It provides the first derivation of elliptic recurrence formulas for all 4-point superconformal blocks in N=1 SCFT, expanding the computational toolkit.

Findings

Derived elliptic recurrence relations for all superconformal blocks

Numerically verified crossing symmetry in N=1 super Liouville theory

Extended the understanding of superconformal bootstrap methods

Abstract

All types of 4-point spheric conformal blocks in both sectors of N=1 superconformal field theory are introduced and analyzed. The elliptic recurrence formulae are derived for all the types of blocks not previously discussed in the literature. The results are used for numerical verification of the crossing symmetry of some 4-point functions in the N=1 superconformal Liouville field theory.