Supersymmetric Embedding of the Quantum Hall Matrix Model

TL;DR

This paper extends the quantum Hall matrix model to include supersymmetry, combining bosonic and fermionic particles, and analyzes how supersymmetry affects the ground state and filling factors.

Contribution

It introduces a supersymmetric version of the quantum Hall matrix model with two particle types and solves the associated constraints, revealing new degrees of freedom and quantum corrections.

Findings

Supersymmetric model includes two phases with bosons and fermions.

Ground state solutions involve new parameters affecting the filling factor.

Quantum corrections to the classical filling factor are exactly canceled by fermionic contributions.

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.