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We consider the partition function of the superconformal Chern-Simonstheories with the quiver diagram being the affine D-type Dynkin diagram.Rewriting the partition function into that of a Fermi gas system, we show thatthe perturbative expansions in 1/N are summed up to an Airy function, as in theABJM theory or more generally the theories of the affine A-type quiver. As acorollary, this provides a proof for the previous proposal in the large Nlimit. For special values of the Chern-Simons levels, we further identify threespecies of the membrane instantons and also conjecture an exact expression ofthe overall constant, which corresponds to the constant map in the topologicalstring theory.

Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas