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tokens: probably also affects the density distribution along the loop and is the reason that we scaled our model emission nonlinearly with a power of 0.4 in Fig. 2 (while the observations are scaled closer to linear with a power of 0.7). The loops in our model corona look more like those in a potential field than like the loops in the observations. In our model we only prescribed the vertical component of the magnetic field, but not the horizontal component (which is not available at 45 s cadence and for this large field of view with HMI). We would therefore miss any helical component of the magnetic field, which would lead to a more twisted appearance of the magnetic field. Moreover, this would increase the energy input into the system and thus help alleviate the problem described above, at least to some extent. Finally, we assume periodic boundary conditions in our model (as do most other 3D MHD models of the solar atmosphere). This implies that the field lines of the fan loops on the western (right) side of the active region leave the box on that side and enter the box again on the other side. In the model, the fan loops therefore connect to an active region (different from the first). On the real Sun, such a connected active region would be far away, at a distance that is far larger than the size of an active region. We tried to account for this in the model by surrounding the active region by enough quiet Sun, so that the appearance of the fan loops is hopefully realistic. None of the above limitations are expected to alter the main conclusion of our study: our data-driven model can account for the structures seen on the real Sun. Future models will have to address these remaining problems step by step, however. 6. Conclusions We showed that we can reproduce many aspects of the corona above an active region using a data-driven 3D MHD model. The emission that we synthesized from the model qualitatively reproduces the observed coronal features of this active region: long loops, fan-like loops, and small transient loops in the active region core. We also showed that these model features are embedded in a diffuse background of coronal emission, as is the case on the real Sun, where a typical loop has a low contrast of only 10% to 30% to the background. Our data-driven model shows that the structure of the observed photospheric magnetic field and its temporal evolution fully govern the appearance of the corona in an active region. Driving the magnetic field at the surface induces currents in the corona at just the correct places: here the plasma is heated and forms EUV loops in the model at exactly the same place where they also appear in the real observations. The energy input in our model is solely based on the driving of the magnetic field and is thus very similar to the scenarios of field-line braiding ( Parker 1988 ) and flux-tube tectonics scenarios ( Priest et al. 2002 ). The success of our model therefore supports these heating scenarios. The