Direct derivation of "mirror" ABJ partition function

Abstract

We study the partition function of the three-dimensional N=6 U(N)_k x U(N+M)_{-k} superconformal Chern-Simons matter theory known as the ABJ theory. We prove that the ABJ partition function on S^3 is exactly the same as a formula recently proposed by Awata, Hirano and Shigemori. While this formula was previously obtained by an analytic continuation from the L(2,1) lens space matrix model, we directly derive this by using a generalization of the Cauchy determinant identity. We also give an interpretation for the formula from brane picture.

12 pages, no figure; v2: minor corrections, references added; v3: typos corrected

References in corpus (12)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Notes on SUSY Gauge Theories on Three-Sphere
• Seiberg Duality in Chern-Simons Theory
• Non-perturbative effects and the refined topological string
• Summing Up All Genus Free Energy of ABJM Matrix Model
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• Exact ABJM Partition Function from TBA
• ABJM Wilson Loops in Arbitrary Representations
• Instanton effects and quantum spectral curves
• Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ Isometry
• Localization on round sphere revisited

Cited by in corpus (51)

• Matrix models from operators and topological strings, 2
• Probing non-perturbative effects in M-theory
• Exact results on ABJ theory and the refined topological string
• Solving M-theory with the Conformal Bootstrap
• Higgs branch localization of 3d N=2 theories
• Matrix models from operators and topological strings
• ABJ Fractional Brane from ABJM Wilson Loop
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• M-theoretic matrix models
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Instanton Effects in Orbifold ABJM Theory
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• ABJM on ellipsoid and topological strings
• Interacting systems and wormholes
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• Exact relations between M2-brane theories with and without Orientifolds
• Exact Instanton Expansion of ABJM Partition Function
• Localization at large N in Chern-Simons-matter theories
• On the Exact Interpolating Function in ABJ Theory
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Orientifolding of the ABJ Fermi gas
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• A matrix model for the latitude Wilson loop in ABJM theory
• ABJ Wilson loops and Seiberg Duality
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• ABJ Quadrality
• Hanany-Witten Transition in Quantum Curves
• Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories
• Localization and Duality for ABJM Latitude Wilson Loops
• Exact results for ABJ Wilson loops and open-closed duality
• Fermi gas approach to general rank theories and quantum curves
• The spectral problem of the ABJ Fermi gas
• Two-Point Functions in ABJM Matrix Model
• Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual
• SU(N) q-Toda equations from mass deformed ABJM theory
• Non-perturbative Tests of Duality Cascades in Three Dimensional Supersymmetric Gauge Theories
• ABJ Theory in the Higher Spin Limit
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• Duality Cascades and Affine Weyl Groups
• 3d dualities with decoupled sectors and brane transitions
• Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• Topological phase, spin Chern-Simons theory and level rank duality on lens space