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

TL;DR

This paper computes the modular transformation matrix for one-point conformal blocks in the NS sector of N=1 super Liouville theory, using integral identities of supersymmetric hyperbolic gamma functions.

Contribution

It provides an explicit integral formula for the modular transformation matrix in the NS sector of super Liouville theory, advancing understanding of its conformal blocks.

Findings

Derived explicit integral expression for the modular matrix.

Utilized chain of integral identities for supersymmetric gamma functions.

Facilitated further analysis of super Liouville conformal blocks.

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.