2d small N=4 Long-multiplet superconformal block

TL;DR

This paper develops superconformal blocks for 2d N=4 theories using the super Virasoro algebra, enabling advanced numerical bootstrap analysis with more constraints than BPS-based methods.

Contribution

It derives the superconformal blocks for long multiplets and formulates crossing equations using both algebraic and superspace approaches, expanding bootstrap tools.

Findings

Derived superconformal blocks for long multiplets.

Set up crossing equations for non-BPS 4-point functions.

Proposed an alternative derivation method using N=4 superspace.

Abstract

We study 2d N=4 superconformal field theories, focusing on its application on numerical bootstrap study. We derive the superconformal block by utilizing the global part of the super Virasoro algebra and set up the crossing equations for the non-BPS long-multiplet 4-point function. Along the way, we build global N=4 superconformal short and long multiplets, and compute all possible 2,3-point functions of long-multiplets that are needed to construct the superconformal blocks and the crossing equations. Since we consider a long-multiplet 4-point function, the number of crossing equations is huge and we expect it to give a strong constraint than the usual superconformal bootstrap analysis, which relies on BPS 4-point functions. In addition, we present an alternative way to derive crossing equations using N=4 superspace and comment on a puzzle.