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.
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Lee, BH., Ro, D. & Yang, H.S. Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory. J. High Energ. Phys. 2017, 39 (2017). https://doi.org/10.1007/JHEP01(2017)039
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DOI: https://doi.org/10.1007/JHEP01(2017)039