N=1 SUSY Conformal Block Recursive Relations

TL;DR

This paper develops recursive relations for superconformal blocks in N=1 supersymmetric theories, enabling efficient numerical analysis of four-point functions within the bootstrap framework.

Contribution

It introduces explicit recursive relations for superconformal blocks based on their analytic properties, advancing computational methods in superconformal field theory.

Findings

Recursive relations match known analytic expressions for special cases.

The method improves numerical studies of four-point functions in superconformal theories.

Facilitates bootstrap analysis in supersymmetric contexts.

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.