  After averaging over fermion couplings, SYK has a collective field
description that sometimes has "wormhole" solutions. We study the fate of these
wormholes when the couplings are fixed. Working mainly in a simple model, we
find that the wormhole saddles persist, but that new saddles also appear
elsewhere in the integration space -- "half-wormholes." The wormhole
contributions depend only weakly on the specific choice of couplings, while the
half-wormhole contributions are strongly sensitive. The half-wormholes are
crucial for factorization of decoupled systems with fixed couplings, but they
vanish after averaging, leaving the non-factorizing wormhole behind.
