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We extend the Fermi gas approach to a class of ABJM-like necklace quivertheories 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. Wedemonstrate the presence of this phase both analytically and numerically in thecase of a three node quiver.

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