We consider the partition function of the superconformal Chern-Simons
theories with the quiver diagram being the affine D-type Dynkin diagram.
Rewriting the partition function into that of a Fermi gas system, we show that
the perturbative expansions in 1/N are summed up to an Airy function, as in the
ABJM theory or more generally the theories of the affine A-type quiver. As a
corollary, this provides a proof for the previous proposal in the large N
limit. For special values of the Chern-Simons levels, we further identify three
species of the membrane instantons and also conjecture an exact expression of
the overall constant, which corresponds to the constant map in the topological
string theory.Comment: 23 pages, 4 figures; v2: section 4.2 added, one figure adde
