We find that a gauged matrix model of rectangular fermionic matrices (amatrix version of the fermion harmonic oscillator) realizes a quantum halldroplet with manifest particle-hole symmetry. The droplet consists of freefermions on the topology of a sphere. It is also possible to deform theHamiltonian by double trace operators, and we argue that this device canproduce two body potentials which might lead the system to realize a fractionalquantum hall state on the sphere. We also argue that a single gauged fermionicquantum mechanics of hermitian matrices realizes a droplet with an edge thathas $c=1/2$ CFT on it.
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机译：我们发现，矩形费米子矩阵（费米子谐振子的矩阵版本）的规范矩阵模型实现了具有明显的粒子-孔对称性的量子滴。液滴由球体拓扑上的自由铁构成。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状态。我们还认为，厄米矩阵的单规范费米子量子力学实现了其边缘具有$ c = 1/2 $ CFT的液滴。
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