Symmetries of the refined D1/D5 BPS spectrum

TL;DR

This paper analyzes the refined BPS spectrum of symmetric orbifold CFTs at large N, revealing a unique degeneracy pattern and exploring the influence of discrete symmetries, including Conway groups, on the spectrum.

Contribution

It uncovers a novel degeneracy property in the spectrum and investigates the role of discrete symmetry groups, including potential larger groups, in the large N limit.

Findings

Degeneracy depends on a linear combination of quantum numbers

Spectrum decomposition satisfies an unusual property

Discrete symmetry groups influence degeneracies

Abstract

We examine the large $N$ 1/4-BPS spectrum of the symmetric orbifold CFT Sym$^N(M)$ deformed to the supergravity point in moduli space for $M= K3$ and $T^4$. We consider refinement under both left- and right-moving $SU(2)_R$ symmetries of the superconformal algebra, and decompose the spectrum into characters of the algebra. We find that at large $N$ the character decomposition satisfies an unusual property, in which the degeneracy only depends on a certain linear combination of left- and right-moving quantum numbers, suggesting deeper symmetry structure. Furthermore, we consider the action of discrete symmetry groups on these degeneracies, where certain subgroups of the Conway group are known to play a role. We also comment on the potential for larger discrete symmetry groups to appear in the large $N$ limit.