Orientifolding of the ABJ Fermi gas

TL;DR

This paper studies the orientifolding of ABJ Fermi gas systems by analyzing their grand partition functions, revealing new exact forms, perturbative coefficients, and functional relations, especially for specific Chern-Simons levels.

Contribution

It provides a systematic WKB analysis of orientifold ABJ theories, deriving explicit grand partition functions and confirming conjectured functional relations for certain levels.

Findings

Derived explicit grand partition functions for orientifold ABJ theories at specific levels

Identified and computed half-instanton corrections from the twisted sector

Proved functional relations among grand partition functions for levels 2 and 4

Abstract

The grand partition functions of ABJ theory can be factorized into even and odd parts under the reflection of fermion coordinate in the Fermi gas approach. In some cases, the even/odd part of ABJ grand partition function is equal to that of $\mathcal{N}=5$ $O(n)\times USp(n')$ theory, hence it is natural to think of the even/odd projection of grand partition function as an orientifolding of ABJ Fermi gas system. By a systematic WKB analysis, we determine the coefficients in the perturbative part of grand potential of such orientifold ABJ theory. We also find the exact form of the first few "half-instanton" corrections coming from the twisted sector of the reflection of fermion coordinate. For the Chern-Simons level $k=2,4,8$ we find closed form expressions of the grand partition functions of orientifold ABJ theory, and for $k=2,4$ we prove the functional relations among the grand partition functions conjectured in arXiv:1410.7658.