We find that a gauged matrix model of rectangular fermionic matrices (a matrix version of the fermion harmonic oscillator) realizes a quantum hall droplet with manifest particle-hole symmetry. The droplet consists of free fermions on the topology of a sphere. It is also possible to deform the Hamiltonian by double trace operators, and we argue that this device can produce two body potentials which might lead the system to realize a fractional quantum hall state on the sphere. We also argue that a single gauged fermionic quantum mechanics of Hermitian matrices realizes a droplet with an edge that has $c=1/2\mathrm{CFT}$ on it.

• Received 1 December 2004

DOI:https://doi.org/10.1103/PhysRevD.71.085001