On Half-BPS States of the ABJM Theory

We analyze SU(2) invariant half-BPS states of the 3d, N = 8 or N = 6 SCFT within the radial quantization of the ABJM theory [1], the theory proposed to describe N M2-branes in the R × C/Zk background. After studying the classical moduli space of these configurations, we explicitly construct a set of gauge invariant operators involving ’t Hooft monopole operators corresponding to these states. We show there is a one–to–one correspondence between the two sets carrying R-charge J and that they are labeled by Young tableaux of J boxes with a maximum of N rows. Restricting the full path integral to this half-BPS sector of the theory, we show the latter is described in terms of N fermions in a 2d harmonic potential in the sector of vanishing angular momentum. The same classification, though in the N → ∞ limit, arise from the plane-wave (BMN) Matrix theory as well as the 11 dimensional LLM bubbling geometries [2], providing supportive evidence for the ABJM theory and/or the Matrix model.