Noncommutative U(1) Gauge Theory As a Non-Linear Sigma Model

TL;DR

This paper demonstrates that 4D noncommutative U(1) gauge theory can be mapped to a solvable 2D non-linear sigma model, providing exact beta functions and linking classical gauge theories to lower-dimensional models.

Contribution

It establishes a novel equivalence between noncommutative 4D U(1) gauge theory and a 2D non-linear sigma model, including exact beta function calculations.

Findings

Exact beta function for the 2D sigma model is derived.

Noncommutative U(1) gauge theory in 4D is equivalent to a solvable 2D model.

Classical U(n) gauge theory on R^{d-2}×R^2_θ approximates lower-dimensional Georgi-Glashow models.

Abstract

Noncommutative U(1) gauge theory in 4-dimensions is shown to be equivalent in some scaling limit to an ordinary non-linear sigma model in 2-dimensions . The model in this regime is solvable and the corresponding exact beta function is found. We also show that classical U(n) gauge theory on {R}^{d-2}{\times}{R}^2_{\theta} can be approximated by a sequence of ordinary (d-2)-dimensional Georgi-Glashow models with gauge groups U(n(L+1)) where L+1 is the matrix size of the regularized noncommutative plane {R}^2_{\theta}.