A holographic approach to the six-dimensional superconformal index

TL;DR

This paper proposes a holographic framework for understanding the superconformal index of six-dimensional theories using twisted holography and super Lie algebra modules, providing explicit formulas for these indices.

Contribution

It introduces a conjectural holographic description of local operators in 6D superconformal theories via the minimal twist of supergravity, leading to new formulas for the superconformal index.

Findings

Local operators form modules for the super Lie algebra $E(3|6)$

Derived closed-formulas for the superconformal index of 6D $ ext{(2,0)}$ theories

Connects twisted holography with super Lie algebra representations

Abstract

We present a conjectural description of the space of local operators on a stack of finitely many fivebranes in $M$ theory at the level of the holomorphic twist. Our approach is through the lens of twisted holography and utilizes a description of the minimal twist of eleven-dimensional supergravity. We find that the spaces of local operators are modules for the exceptional linearly compact super Lie algebra $E(3|6)$. From the conjectural description of local operators we deduce closed formulas for the superconformal index of six-dimensional $\mathcal{N}=(2,0)$ theories of type $A_{N-1}$.