On Half-BPS States of the ABJM Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0904.4605,
title = {On Half-BPS States of the ABJM Theory},
author = {M. M. Sheikh-Jabbari and Joan Simon},
journal= {arXiv preprint arXiv:0904.4605},
year = {2009}
}
Comments
24 pages, 3 figures, v2: a reference added