Abstract
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.
Highlights
We consider the partition function of the superconformal Chern-Simons theories with the quiver diagram being the affine D-type Dynkin diagram
In [15] the authors showed that the Fermi gas formalism works for theories of general A-type quivers, and that the completion by an Airy function is universal for these theories
In this paper we have studied the partition function of the N = 3 superconformal ChernSimons theories of the D-type quiver, and have shown that we can rewrite the partition function into that of the Fermi gas system as in the case of the A-type quiver
Summary
We shall present a Fermi gas description for the superconformal ChernSimons theories of the D-type quiver. The denominator H, coming from the hypermultiplets in the bifundamental representation, is
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