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

TL;DR

This paper analyzes the partition functions of superconformal Chern-Simons theories with affine D-type quivers, showing they can be expressed as Airy functions and identifying membrane instantons, thus extending known results from affine A-type theories.

Contribution

It demonstrates that the partition functions for affine D-type quiver theories can be summed into an Airy function and provides a proof for the large N behavior, also identifying membrane instantons for special levels.

Findings

Partition functions sum to an Airy function in the large N limit.

Identification of three species of membrane instantons at special levels.

Conjecture of an exact constant related to topological string theory.

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.