Generation of 4d Gauge Theory and Gravity from their 3d   versions--Asymptotic Disappearance of Space and Time (ADST) Scenario--
  An exotic scenario of our universe is proposed in which our universe starts from zero space-time dimensions (0d), namely, a set of discrete points, it increases the (continuous) dimensionality during the cooling down of it, and finally arrives at the present four space-time dimensions (4d). This scenario may be called asymptotic disappearance (or discretization) of space-time (ADST) scenario. The final stage of the scenario is to generate dynamically 4d from the 3d, which is shown to be possible for both gauge theory and gravity, including the standard model. To examine the validity of the scenario, 4d QED generated from its 3d version at high energy is studied, in which one spatial dimension is discretized with a lattice constant $a$. From the LEP2 experiment on $e^+ e^- \to \gamma \gamma$, $a$ is constrained to satisfy $a \le 461$ GeV. Expected bound on $a$ at future $e^+ e^-$ linear collider is discussed. The finite size of $a$ modifies the dispersion relation, causing the violation of Lorentz symmetry. Then, the paradox of observing 20 TeV $\gamma$ rays from the active galaxy Markarian 501 may disappear, overcoming the GZK cut. 
A. Sugamoto (Ochanomizu U.)