Supersymmetric Embedding of the Quantum Hall Matrix Model

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 $\nu$ receives no quantum correction. We conclude that the Polychronakos effect is exactly compensated by the opposite fermionic contributions.

30 pages, 3 tables

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