S-move matrix in the NS sector of $N=1$ super Liouville field theory

Abstract: In this paper we calculate matrix of modular transformations of the one-point toric conformal blocks in the Neveu-Schwarz sector of $N=1$ super Liouville field theory. For this purpose we use explicit expression for this matrix as integral of product of certain elements of fusion matrix. This integral is computed using the chain of integral identities for supersymmetric hyperbolic gamma functions derived by the degeneration of the integrals of parafermionic elliptic gamma functions.