Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks

TL;DR

This paper constructs braiding and fusion matrices for Neveu-Schwarz super-conformal blocks, enabling explicit verification of the bootstrap equation in N=1 supersymmetric Liouville field theory, thus advancing understanding of super-conformal field theories.

Contribution

It generalizes the method used for Virasoro blocks to super-conformal blocks, providing explicit matrices and verifying the bootstrap equation in the NS sector.

Findings

Explicit braiding and fusion matrices for NS super-conformal blocks

Verification of the bootstrap equation in N=1 supersymmetric Liouville theory

Extension of Virasoro conformal block methods to super-conformal case

Abstract

We construct, generalizing appropriately the method applied by J. Teschner in the case of the Virasoro conformal blocks, the braiding and fusion matrices of the Neveu-Schwarz super-conformal blocks. Their properties allow for an explicit verification of the bootstrap equation in the NS sector of the N=1 supersymmetric Liouville field theory.