Supersymmetric gauged matrix models from dimensional reduction on a sphere

It was recently proposed that $N=1$ supersymmetric gauged matrix models have a duality of order four — that is, a quadrality — reminiscent of infrared dualities of SQCD theories in higher dimensions. In this note, we show that the zero-dimensional quadrality proposal can be inferred from the two-dimensional Gadde-Gukov-Putrov triality. We consider two-dimensional $N=(0,2)$ SQCD compactified on a sphere with the half-topological twist. For a convenient choice of $R$-charge, the zero-mode sector on the sphere gives rise to a simple $N=1$ gauged matrix model. Triality on the sphere then implies a triality relation for the supersymmetric matrix model, which can be completed to the full quadrality.