  We attempt to construct eternal traversable wormholes connecting two
asymptotically AdS regions by introducing a static coupling between their dual
CFTs. We prove that there are no semiclassical traversable wormholes with
Poincar\'e invariance in the boundary directions in higher than two spacetime
dimensions. We critically examine the possibility of evading our result by
coupling a large number of bulk fields. Static, traversable wormholes with less
symmetry may be possible, and could be constructed using the ingredients we
develop here.
