  We study the partition functions of multiple replicas (copies) of D-brane
configurations in the type IIB (IKKT) matrix model. We consider the quenched
regime, where small fluctuations of the matrices are superimposed onto the slow
(quenched) dynamics of the background, so the partition function is an ensemble
average over the background. Interacting D-branes always factorize in a simple
way. On the other hand, the non-interacting BPS configurations may or may not
factorize depending on the number of replicas, and their factorization
mechanism is more involved as the corresponding saddle-point solutions
(half-wormholes) break the replica symmetry. We argue that the simple
factorization mechanism of interacting branes is actually more interesting as
it carries the specific signatures of quantum gravity, which are absent from
disordered field theories like the SYK model.
