M2-branes and plane partitions

Abstract

There is a correspondence between the protected local operators in the 3d SCFTs describing the geometry ${\mathbb{C}}^2$ probed by a stack of $N$ M2-branes and plane partitions of trace $N$. We give combinatorial expressions of the indices which count the local operators parametrizing ${\mathbb{C}}^2/{\mathbb{Z}}_k$ probed by $N$ M2-branes in the canonical and grand canonical ensembles in terms of generating functions for plane partitions. We derive the asymptotic behaviors of the grand potential in the high-temperature limit and the scaling dimension in the large $N$ limit.

30 pages, v3: published version in JHEP

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Cited by in corpus (6)

• $\mathcal{N}=2^{\ast }$ Schur indices
• Exact Stringy Microstates from Gauge Theories
• Dualities and flavored indices of M2-brane SCFTs
• ADHM Wilson line defect indices
• Asymptotic degeneracies of M2-brane SCFTs
• Supersymmetric zeta functions and determinants