# Kac-Moody algebras from M5-giants

## TL;DR

This paper explores the structure of Higgs indices in 3d $ ext{N}=4$ $U(N)$ ADHM theories, revealing connections to Kac-Moody and W-algebras through giant graviton expansions and confirming index consistency.

## Contribution

It uncovers the algebraic structures underlying M5-brane giant graviton indices, linking them to generalized W-algebra characters and affine Kac-Moody algebras, and verifies the inverse expansion consistency.

## Key findings

- Indices involve generalized W-algebra characters
- Indices include affine Kac-Moody algebra characters
- Inverse expansions reproduce original Higgs indices

## Abstract

We examine the giant graviton expansions of the Higgs indices for the 3d $\mathcal{N}=4$ $U(N)$ ADHM theories with $l$ fundamental hypermultiplets. The indices for the M5-brane giant gravitons of wrapping number $m$ appearing in the expansions consist of the contributions that generalize the characters of the W-algebra $\mathcal{W}(\mathfrak{gl}(m))$ and those which realize the characters of the affine Kac-Moody algebras of type $A_{l-1}$. Also we confirm that the inverse giant graviton expansions of the resulting M5-brane indices consistently reproduce the Higgs indices.