  In this paper, we introduce a "partially disorder-averaged" SYK model. This
model has a real parameter that smoothly interpolates between the ordinary
totally disorder-averaged SYK model and the totally fixed-coupling model. For
the large $N$ effective description, in addition to the usual bi-local
collective fields, we also introduce a new additional set of local collective
fields. These local fields can be understood as "half" of the bi-local
collective fields, and in the totally fixed-coupling limit, they represent the
"half-wormholes" which were found in recent studies. We find that the large $N$
saddles of these local fields vanish in the total-disorder-averaged limit,
while they develop nontrivial profiles as we gradually fix the coupling
constants. We argue that the bulk picture of these local collective fields
represents a correlation between a spacetime brane and the asymptotic AdS
boundary. This illuminates how the half-wormhole saddles emerge in the SYK
model with fixed couplings.
