M2-branes and plane partitions

Tadashi Okazaki

doi:10.1007/jhep07(2022)028

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arXiv · 2204.01973

M2-branes and plane partitions

Tadashi Okazaki

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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.

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Tadashi Okazaki. 2022-04-05. M2-branes and plane partitions. https://doi.org/10.1007/jhep07(2022)028

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