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

Journal of High Energy Physics, Jan 2017

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.

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Bum-Hoon Lee, Daeho Ro, Hyun Seok Yang. Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory, Journal of High Energy Physics, 2017, 39, DOI: 10.1007/JHEP01(2017)039