Super Yang-Mills Theory as a Twistor Matrix Model

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We introduce a covariant finite regulator for N = 4 super Yang-Mills theory on S⁴. Our formulation is based on holomorphic Chern-Simons theory on twistor space. By switching on a large background flux, the twistor space dissolves into a fuzzy geometry, with a finite number of points. The large N continuum limit of the matrix model naturally approaches ordinary N = 4 SYM. We comment on the relation between our model and the 4D quantum Hall effect.