c-Recursion for multi-point superconformal blocks. NS sector

TL;DR

This paper introduces a recursive method for calculating multi-point superconformal blocks in the NS sector, extending previous Virasoro algebra results to superconformal cases with improved computational efficiency.

Contribution

It generalizes recursive techniques to superconformal blocks, analyzing their analytic properties and asymptotics for efficient multi-point computations on various topologies.

Findings

Applicable to genus zero and one surfaces with multiple punctures

Provides a more efficient recursive computation method

Extends techniques from Virasoro to superconformal blocks

Abstract

We develop a recursive approach to computing Neveu-Schwarz conformal blocks associated with n-punctured Riemann surfaces. This work generalizes the results of [1] obtained recently for the Virasoro algebra. The method is based on the analysis of the analytic properties of the superconformal blocks considered as functions of the central charge c. It consists of two main ingredients: the study of the singular behavior of the conformal blocks and the analysis of their asymptotic properties when c tends to infinity. The proposed construction is applicable for computing multi-point blocks in different topologies. We consider some examples for genus zero and one with different numbers of punctures. As a by-product, we propose a new way to solve the recursion relations, which gives more efficient computational procedure and can be applied to SCFT case as well as to pure Virasoro blocks.