Strong Coupling Phenomena on the Noncommutative Plane

TL;DR

This paper investigates strong coupling effects in non-commutative U(1) gauge theory, revealing modifications to light speed and photon stability, using T-duality and large N limits, and introduces an exotic open string theory in a specific limit.

Contribution

It provides a novel analysis of strong coupling phenomena in non-commutative gauge theories using T-duality and large N limits, highlighting new physical effects and limits.

Findings

High frequency light speed is modified by a factor involving the non-commutative parameter.

Photon momentum in non-commutative directions has an upper bound due to pair production.

A special $ heta oty$ limit leads to an exotic open string theory.

Abstract

We study strong coupling phenomena in U(1) gauge theory on the non-commutative plane. To do so, we make use of a T-dual description in terms of an $N\to\infty$ limit of U(N) gauge theory on a commutative torus. The magnetic flux on this torus is taken to be $m=N-1$, while the area scales like 1/N, keeping $\Lambda_{QCD}$ fixed. With a few assumptions, we argue that the speed of high frequency light in pure non-commutative QED is modified in the non-commutative directions by the factor $1 + \Lambda_{QCD}^4 \theta^2$, where $\theta$ is the non-commutative parameter. If charged flavours are included, there is an upper bound on the momentum of a photon propagating in the non-commutative directions, beyond which it is unstable against production of charged pairs. We also discuss a particular $\theta\to\infty$ limit of pure non-commutative QED which is T-dual to a more conventional $N\to\infty$ limit with $m/N$ fixed. In the non-commutative description, this limit gives rise to an exotic theory of open strings.