Corrections of an elliptic block in the NS sector

TL;DR

This paper introduces a correction to an elliptic block in the NS sector of 2d superconformal field theories, validated through numerical checks and consistency with crossing symmetries.

Contribution

It provides a necessary correction to the elliptic block in the NS sector and verifies it via numerical and recursive methods.

Findings

The correction is essential for the consistency of the elliptic block.

Numerical checks confirm the validity of the corrected formula.

The correction aligns with crossing symmetry and recursion results.

Abstract

We propose a correction to one of the elliptic blocks in the NS sector of 2d $\mathcal N = 1$ superconformal field theories. We analyze the 4-point block in the pillow geometry to demonstrate the necessity of the correction and verify the formula by numerically checking the crossing symmetries in the $\mathcal N =1 $ super Liouville theory, as well as directly comparing the $c$-recursion and $h$-recursion results.