M2-branes and plane partitions

Abstract

Abstract There is a correspondence between the protected local operators in the 3d SCFTs describing the geometry ℂ2 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 ℂ2/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.

Keywords

• Brane Dynamics in Gauge Theories
• M-Theory
• Supersymmetric Gauge Theory