Strong Coupling Phenomena on the Noncommutative Plane

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.

24 pages, latex, 2 figures, corrected typo in eqn 6.6

References in corpus (6)

• Testing Non-commutative QED, Constructing Non-commutative MHD
• Comments on Non-Commutative Phenomenology
• Superluminal Noncommutative Photons
• Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions
• Supergravity couplings to Noncommutative Branes, Open Wilson Lines and Generalised Star Products
• Aspects of Gauge Theory on Commutative and Noncommutative Tori

Cited by in corpus (2)

• Lectures on Two-Dimensional Noncommutative Gauge Theory 2: Quantization
• Wilson line correlators in two-dimensional noncommutative Yang-Mills theory