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

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 non-commutative 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.