Title: Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory
Abstract: We study localization of five-dimensional supersymmetric U(1) gauge theory on $$ {\mathbb{S}}^3\times {\mathbb{R}}_{\theta}^2 $$ where $$ {\mathbb{R}}_{\theta}^2 $$ is a noncommutative (NC) plane. The theory can be isomorphically mapped to three-dimensional supersymmetric U(N → ∞) gauge theory on $$ {\mathbb{S}}^3 $$ using the matrix representation on a separable Hilbert space on which NC fields linearly act. Therefore the NC space $$ {\mathbb{R}}_{\theta}^2 $$ allows for a flexible path to derive matrix models via localization from a higher-dimensional supersymmetric NC U(1) gauge theory. The result shows a rich duality between NC U(1) gauge theories and large N matrix models in various dimensions.