On Half-BPS States of the ABJM Theory

TL;DR

This paper classifies half-BPS states in the ABJM theory, linking gauge-invariant operators, Young tableaux, and fermionic descriptions, and connects these findings to dual geometries and matrix models.

Contribution

It explicitly constructs gauge-invariant operators for half-BPS states in ABJM theory and establishes a one-to-one correspondence with Young tableaux, linking field theory, matrix models, and gravity duals.

Findings

BPS states correspond to Young tableaux with J boxes and N rows.

Half-BPS sector reduces to N fermions in a 2D harmonic potential.

Results support the duality between ABJM theory, matrix models, and gravity geometries.

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.