On the Renormalizability of Noncommutative U(1) Gauge Theory - an Algebraic Approach

TL;DR

This paper studies the renormalizability of a noncommutative U(1) gauge theory by algebraically localizing a nonlocal operator using BRST doublets, aiming to address infrared issues without adding extra degrees of freedom.

Contribution

It introduces a localization method for a nonlocal operator in noncommutative gauge theory using BRST doublets, enabling a complete algebraic renormalization analysis.

Findings

Successful localization of the operator without extra degrees of freedom

Complete algebraic proof of renormalizability

Framework for addressing infrared problems in noncommutative gauge theories

Abstract

We investigate the quantum effects of the nonlocal gauge invariant operator $\frac{1}{{}{D}^{2}}{F}_{\mu \nu}\ast \frac{1}{{}{D}^{2}}{F}^{\mu \nu}$ in the noncommutative U(1) action and its consequences to the infrared sector of the theory. Nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the Lorentz invariance. More recently, a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field, and the first loop analysis was carried out $(Eur.Phys.J.\textbf{C62}:433-443,2009)$. We will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only BRST doublets. This will allow us to make a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT.