On Half-BPS States of the ABJM Theory

Details On Half-BPS States of the ABJM Theory On Half-BPS States of the ABJM Theory

2009-04-29

arxiv.org/abs/0904.4605v2

JHEP 0908:073,2009

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 3 figures, v2: a reference added

Scientific paper

10.1088/1126-6708/2009/08/073

We analyze SU(2) invariant half-BPS states of the 3d \cN=8 or \cN=6 SCFT within the radial quantization of the ABJM theory, the theory proposed to describe N M2-branes in the R^3x C^4/Z_k 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 to infinity limit, arise from the plane-wave (BMN) Matrix theory as well as the 11 dimensional LLM bubbling geometries, providing supportive evidence for the ABJM theory and/or the Matrix model.

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