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 $c=1/2$ CFT on it.
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机译：我们发现，矩形费米子矩阵的规范矩阵模型（费米子谐波振荡器的矩阵版本）实现了具有明显粒子-孔对称性的量子霍尔液滴。液滴由球体拓扑上的自由费米子组成。也可以通过双迹算符使哈密顿量变形，并且我们认为该设备可以产生两个体势，这可能导致系统在球体上实现分数量子霍尔态。我们还认为，厄米矩阵的单规范费米子量子力学实现了具有$ c = 1/2 $ CFT边缘的液滴。
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