  We construct a nearly-$AdS_2$ solution describing an eternal traversable
wormhole. The solution contains negative null energy generated by quantum
fields under the influence of an external coupling between the two boundaries.
In parallel, we discuss two SYK systems coupled by a relevant interaction. The
physics of the two cases is very similar. They both share a "gravitational"
subsector which is identical. The solution within this subsector sets the stage
for dynamics which is almost conformal invariant. We study this system in
detail, both in gravity and in the SYK model. The coupled SYK models have an
interesting phase diagram at finite temperature, displaying the usual
Hawking-Page transition between the thermal AdS phase at low temperature and
the black hole phase at high temperature. Interestingly, these two phases are
continuously connected in the microcannonical ensemble.
