CERN LEP2 constraint on 4D QED having dynamically generated spatial dimension

We study 4D QED in which one spatial dimension is dynamically generated from 3D action, following the mechanism proposed by Arkani-Hamed, Cohen and Georgi. In this model, the generated fourth dimension is discretized by an interval parameter $a$. We examine the phenomenological constraint on the parameter $a$ coming from the collider experiments on the QED process $e^+ e^- \to \gamma \gamma$. It is found that the LEP2 experiments give the constraint of $1/a \simgt 461\gev$. Expected bound on the same parameter $a$ at the future $e^+ e^-$ linear collider is briefly discussed.