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

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

2005-05-15

arxiv.org/abs/hep-th/0505129v2

Nucl.Phys.B729:467-491,2005

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, 4 figures; v2: A typo fixed, references added

Scientific paper

10.1016/j.nuclphysb.2005.08.042

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.

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