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We study localization of five-dimensional supersymmetric $U(1)$ gauge theoryon $\mathbb{S}^3 \times \mathbb{R}_{\theta}^{2}$ where$\mathbb{R}_{\theta}^{2}$ is a noncommutative (NC) plane. The theory can beisomorphically mapped to three-dimensional supersymmetric $U(N \to \infty)$gauge theory on $\mathbb{S}^3$ using the matrix representation on a separableHilbert space on which NC fields linearly act. Therefore the NC space$\mathbb{R}_{\theta}^{2}$ allows for a flexible path to derive matrix modelsvia localization from a higher-dimensional supersymmetric NC $U(1)$ gaugetheory. The result shows a rich duality between NC $U(1)$ gauge theories andlarge $N$ matrix models in various dimensions.

Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory