Towards Noncommutative Fuzzy QED

TL;DR

This paper investigates noncommutative fuzzy QED in four dimensions, revealing gauge-invariant UV-IR mixing, deriving the beta function, and exploring topology change due to noncommutative interactions.

Contribution

It provides the first analysis of gauge-invariant UV-IR mixing in fuzzy QED on S^2 x S^2 and discusses topology change in noncommutative four-dimensional space.

Findings

Existence of gauge-invariant UV-IR mixing in fuzzy QED.

Derivation of the beta function for the model.

Discussion of topology change due to noncommutative interactions.

Abstract

We study in one-loop perturbation theory noncommutative fuzzy quenched QED_4. We write down the effective action on fuzzy S**2 x S**2 and show the existence of a gauge-invariant UV-IR mixing in the model in the large N planar limit. We also give a derivation of the beta function and comment on the limit of large mass of the normal scalar fields. We also discuss topology change in this 4 fuzzy dimensions arising from the interaction of fields (matrices) with spacetime through its noncommutativity.