LLL vs. LLM: Half BPS Sector of N=4 SYM Equals to Quantum Hall System

TL;DR

This paper explores the deep correspondence between the half BPS sector of N=4 SYM theory and quantum Hall systems, extending models to include particle-quasihole symmetry and shedding light on related string theory phenomena.

Contribution

It establishes a detailed equivalence between N=4 SYM half BPS states and quantum Hall physics, introducing an extended noncommutative Chern-Simons matrix model with particle-quasihole symmetry.

Findings

Equivalence of half BPS states and quantum Hall configurations.

Extension of matrix theory with independent particle and quasihole degrees of freedom.

Insights into giant graviton stability and stringy exclusion principle.

Abstract

In this paper we elaborate on the correspondence between the quantum Hall system with filling factor equal to one and the N=4 SYM theory in the 1/2 BPS sector, previously mentioned in the [hep-th/0409174, hep-th/0409115]. We show the equivalence of the two in various formulations of the quantum Hall physics. We present an extension of the noncommutative Chern-Simons Matrix theory which contains independent degrees of freedom (fields) for particles and quasiholes. The BPS configurations of our model, which is a model with explicit particle-quasihole symmetry, are in one-to-one correspondence with the 1/2 BPS states in the N=4 SYM. Within our model we shed light on some less clear aspects of the physics of the N=4 theory in the 1/2 BPS sector, like the giant dual-giant symmetry, stability of the giant gravitons, and stringy exclusion principle and possible implications of the (fractional) quantum Hall effect for the AdS/CFT correspondence.