  In this note we study the SYK model with one time point, recently considered
by Saad, Shenker, Stanford, and Yao. Working in a collective field description,
they derived a remarkable identity: the square of the partition function with
fixed couplings is well approximated by a "wormhole" saddle plus a "pair of
linked half-wormholes" saddle. It explains factorization of decoupled systems.
Here, we derive an explicit formula for the half-wormhole contribution. It is
expressed through a hyperpfaffian of the tensor of SYK couplings. We then
develop a perturbative expansion around the half-wormhole saddle. This
expansion truncates at a finite order and gives the exact answer. The last term
in the perturbative expansion turns out to coincide with the wormhole
contribution. In this sense the wormhole saddle in this model does not need to
be added separately, but instead can be viewed as a large fluctuation around
the linked half-wormholes.
