The large-N partition function for non-parity-invariant Chern-Simons-matter theories

TL;DR

This paper extends the Fermi gas approach to non-parity-invariant Chern-Simons-matter theories, showing their partition functions on S^3 are Airy functions with a large-N phase, confirmed analytically and numerically.

Contribution

It introduces a generalized Fermi gas method for non-parity-invariant theories and characterizes the large-N phase in their partition functions.

Findings

Partition functions are Airy functions with a phase scaling as Nk.

Analytical and numerical evidence supports the phase presence.

The approach applies to ABJM-like necklace quiver theories without parity symmetry.

Abstract

We extend the Fermi gas approach to a class of ABJM-like necklace quiver theories without parity invariance. The resulting partition function on $S^3$ retains the form of an Airy function, but now includes a phase that scales as $Nk$ in the large-$N$ limit where $k$ is an overall Chern-Simons level. We demonstrate the presence of this phase both analytically and numerically in the case of a three node quiver.