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We analyze SU(2) invariant half-BPS states of the 3d \cN=8 or \cN=6 SCFTwithin the radial quantization of the ABJM theory, the theory proposed todescribe N M2-branes in the R^3x C^4/Z_k background. After studying theclassical moduli space of these configurations, we explicitly construct a setof gauge invariant operators involving 't Hooft monopole operatorscorresponding to these states. We show there is a one--to--one correspondencebetween the two sets carrying R-charge J and that they are labeled by Youngtableaux of J boxes with a maximum of N rows. Restricting the full pathintegral to this half-BPS sector of the theory, we show the latter is describedin terms of N fermions in a 2d harmonic potential in the sector of vanishingangular momentum. The same classification, though in the N to infinity limit,arise from the plane-wave (BMN) Matrix theory as well as the 11 dimensional LLMbubbling geometries, providing supportive evidence for the ABJM theory and/orthe Matrix model.

On Half-BPS States of the ABJM Theory