  We reconsider the role of wormholes in the AdS/CFT correspondence. We focus
on Euclidean wormholes that connect two asymptotically AdS or hyperbolic
regions with $\mathbb{S}^1\times \mathbb{S}^{d-1}$ boundary. There is no
solution to Einstein's equations of this sort, as the wormholes possess a
modulus that runs to infinity. To find on-shell wormholes we must stabilize
this modulus, which we can do by fixing the total energy on the two boundaries.
Such a wormhole gives the saddle point approximation to a non-standard problem
in quantum gravity, where we fix two asymptotic boundaries and constrain the
common energy. Crucially the dual quantity does not factorize even when the
bulk is dual to a single CFT, on account of the fixed energy constraint. From
this quantity we extract a smeared version of the microcanonical spectral form
factor. For a chaotic theory this quantity is self-averaging, i.e.
well-approximated by averaging over energy windows, or over coupling constants.
  We go on to give a precision test involving the microcanonical spectral form
factor where the two replicas have slightly different coupling constants. In
chaotic theories this form factor is known to smoothly decay at a rate
universally predicted in terms of one replica physics, provided that there is
an average either over a window or over couplings. We compute the expected
decay rate for holographic theories, and the form factor from a wormhole, and
the two exactly agree for a wide range of two-derivative effective field
theories in AdS. This gives a precision test of averaging in AdS/CFT.
  Our results interpret a number of confusing facts about wormholes and
factorization in AdS and suggest that we should regard gravitational effective
field theory as a mesoscopic description, analogous to semiclassical mesoscopic
descriptions of quantum chaotic systems.
