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

TL;DR

This paper demonstrates how localization of five-dimensional supersymmetric noncommutative U(1) gauge theory on a specific space leads to matrix models, revealing a duality with large N matrix models in various dimensions.

Contribution

It introduces a method to derive matrix models from higher-dimensional supersymmetric noncommutative gauge theories via localization.

Findings

Localization maps 5D NC U(1) theory to 3D large N gauge theory.

Establishes a duality between NC U(1) theories and large N matrix models.

Provides a new pathway to study matrix models from higher-dimensional theories.

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.