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arXiv · hep-th/0410070

Supersymmetric Embedding of the Quantum Hall Matrix Model

James Gates Jr·Ahmed Jellal·EL Hassan Saidi·Michael Schreiber
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Abstract

We develop a supersymmetric extension of the Susskind-Polychronakos matrix theory for the quantum Hall fluids. This is done by considering a system combining two sets of different particles and using both a component field method as well as world line superfields. Our construction yields a class of models for fractional quantum Hall systems with two phases U and D involving, respectively $N_1$ bosons and $N_2$ fermions. We build the corresponding supersymmetric matrix action, derive and solve the supersymmetric generalization of the Susskind-Polychronakos constraint equations. We show that the general U(N) gauge invariant solution for the ground state involves two configurations parameterized by the bosonic contribution $k_{1}$ (integer) and in addition a new degree of freedom $k_{2}$, which is restricted to 0 and 1. We study in detail the two particular values of $k_{2}$ and show that the classical (Susskind) filling factor $ν$ receives no quantum correction. We conclude that the Polychronakos effect is exactly compensated by the opposite fermionic contributions.

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James Gates Jr, Ahmed Jellal, EL Hassan Saidi, Michael Schreiber. 2004-10-07. Supersymmetric Embedding of the Quantum Hall Matrix Model. https://doi.org/10.1088/1126-6708%2F2004%2F11%2F075

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