  We consider two quenched, chiral ensembles which are coupled in such a way
that a combined chiral symmetry is preserved. The coupling also links the
topology of the two systems such that the number of exact zero modes in the
coupled system equals the sum of the number of zero modes in the two uncoupled
systems counted with sign. The canceled modes that turn non-topological due to
the coupling become near-zero modes at small coupling. We analyze the
distribution of these would-be zero modes using effective field theory. The
distribution is universal and, in the limit of small coupling, the would-be
zero modes are distributed according to a finite size chiral Gaussian ensemble,
where the width of the distribution scales as the inverse square root of the
volume.
