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arXiv · 1609.00753

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

Bum-Hoon Lee·Daeho Ro·Hyun Seok Yang
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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 $U(N \to \infty)$ 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. 2016-09-02. Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory. https://doi.org/10.1007/jhep01(2017)039

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