Do instantons and strings cluster when the number of colors is large?

We consider the N_c → ∞ limit of QCD using a toy model in which instantons exchange color-singlet scalar fields which do not self-interact. Our main observation is that collective attraction leads the formation of large clusters containing O(N_c) nonperturbative objects. We further show that this clustering of instantons is limited due to a non-trivial repulsion inherent in the ADHM multi-instanton solution. As a result the vacuum is very different from that at low N_c, notably being more inhomogeneous, in ways which will affect chiral symmetry breaking of light quarks. We also briefly discuss a similar phenomenon for color strings in baryons made of medium-mass (charm-like) quarks.