On the N=1 super Liouville four-point functions

TL;DR

This paper constructs four-point correlation functions in N=1 SUSY Liouville theory using recursive conformal blocks, verifies their crossing symmetry, and derives differential equations for degenerate cases.

Contribution

It introduces a recursive method for constructing superconformal blocks and applies it to compute four-point functions in N=1 SUSY Liouville theory, including degenerate cases.

Findings

Derived third-order differential equation for degenerate fields.

Numerically verified crossing symmetry of correlation functions.

Constructed explicit four-point functions in the super Liouville theory.

Abstract

We construct the four-point correlation functions containing the top component of the supermultiplet in the Neveu-Schwarz sector of the N=1 SUSY Liouville field theory. The construction is based on the recursive representation for the NS conformal blocks. We test our results in the case where one of the fields is degenerate with a singular vector on the level 3/2. In this case, the correlation function satisfies a third-order ordinary differential equation, which we derive. We numerically verify the crossing symmetry relations for the constructed correlation functions in the nondegenerate case.