Orientifolding of the ABJ Fermi gas

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 $\mathcal{N}=5$ $O(n)\times USp(n^{\prime })$ 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.

71 pages, 2 figures, 38 ancillary files; v2: typos corrected; v3: new results in section 6. footnote 5 added

References in corpus (12)

• Fractional M2-branes
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Probing non-perturbative effects in M-theory
• Exact results on ABJ theory and the refined topological string
• Exact ABJM Partition Function from TBA
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• CFT and topological recursion
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Topological Strings and (Almost) Modular Forms
• Probing non-perturbative effects in M-theory on orientifolds

Cited by in corpus (17)

• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• ABJ Quadrality
• Giambelli Identity in Super Chern-Simons Matrix Model
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Functional Equations and Separation of Variables for Exact g-Function
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
• Exact results for ABJ Wilson loops and open-closed duality
• Two-Point Functions in ABJM Matrix Model
• Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• 3d dualities with decoupled sectors and brane transitions
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas