Asymptotic degeneracies of M2-brane SCFTs

TL;DR

This paper analyzes the asymptotic growth of BPS operator degeneracies in M2-brane SCFTs, revealing a universal $n^{2/3}$ growth pattern and providing explicit formulas for these degeneracies.

Contribution

It derives explicit asymptotic formulas for BPS operator degeneracies in M2-brane SCFTs using large $N$ indices and the Meinardus theorem, uncovering a universal growth behavior.

Findings

Degeneracies grow as $n^{2/3}$ universally across theories.

Explicit coefficients for the $n^{2/3}$ growth are calculated.

Further correction terms to the asymptotic growth are determined.

Abstract

We study the asymptotic growth of the degeneracy of the BPS local operators with scaling dimension $n/2$ in the three-dimensional superconformal field theories describing $N$ M2-branes. From the large $N$ supersymmetric indices we obtain the asymptotic formulas for degeneracies of the M2-brane SCFTs according to the Meinardus theorem. We observe an intriguing universal $n^{2/3}$ growth of the degeneracies in various theories of M2-brane SCFTs. We also determine the coefficients of $n^{2/3}$ growth as well as further corrections in these theories explicitly.