On the super Liouville four-point functions

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.