  We study a two-site Sachdev-Ye-Kitaev (SYK) model with complex couplings, and
identify a low temperature transition to a gapped phase characterized by a
constant in temperature free energy. This transition is observed without
introducing a coupling between the two sites, and only appears after ensemble
average over the complex couplings. We propose a gravity interpretation of
these results by constructing an explicit solution of Jackiw-Teitelboim (JT)
gravity with matter: a two-dimensional Euclidean wormhole whose geometry is the
double trumpet. This solution is sustained by imaginary sources for a marginal
operator, without the need of a coupling between the two boundaries. As the
temperature is decreased, there is a transition from a disconnected phase with
two black holes to the connected wormhole phase, in qualitative agreement with
the SYK observation. The expectation value of the marginal operator is an order
parameter for this transition. This illustrates in a concrete setup how a
Euclidean wormhole can arise from an average over field theory couplings.
