String theory in a scale dependent discontinuous space-time

As remarked by Nobel Laureate Gerardus 't Hooft discrete space-time may be the most radical but logical viewpoint of reality. All the same, string theory is formulated on a continuous smooth space-time. In the present note we show that an effective Lagrangian can be established in a discontinuous space-time. The work which was guided by E-infinity theory seems to confirm this viewpoint.