Asymptotic Degeneracies of M2-Brane SCFTs

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 \(n^{2/3}\) $n^{2/3}$ growth of the degeneracies in various theories of M2-brane SCFTs. We also determine the coefficients of \(n^{2/3}\) $n^{2/3}$ growth as well as further corrections in these theories explicitly.