Exact results on ABJ theory and the refined topological string

Abstract

We study the partition function of the ABJ theory, which is the N=6 superconformal Chern-Simons matter theory with gauge group U(N)xU(N+M) and Chern-Simons levels (k,-k). We exactly compute the ABJ partition function on a three sphere for various k, M and N via the Fermi gas approach. By using these exact data, we show that the ABJ partition function is completely determined by the refined topological string on local P^1 x P^1, including membrane instanton effects in the M-theory dual.

arXiv comment24+29 pages, 4 figures; v2:minor improvements

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• The Large N Limit of Superconformal Field Theories and Supergravity
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Fivebranes, Membranes and Non-Perturbative String Theory
• Fractional M2-branes
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• The Exact Superconformal R-Symmetry Extremizes Z
• The Refined Topological Vertex
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• N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds
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• Seiberg Duality in Chern-Simons Theory
• ABJM theory as a Fermi gas
• Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions
• Multi-Matrix Models and Tri-Sasaki Einstein Spaces
• Non-perturbative effects and the refined topological string
• Nonperturbative aspects of ABJM theory
• Matrix Model as a Mirror of Chern-Simons Theory
• Nonperturbative Tests of Three-Dimensional Dualities
• Exact Results in ABJM Theory from Topological Strings
• Chern-Simons Theory and Topological Strings
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
• Instanton Effects in ABJM Theory from Fermi Gas Approach
• Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity
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• Perturbative Analysis of Gauged Matrix Models
• Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
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• Membrane instantons from a semiclassical TBA
• Branes and Supersymmetry Breaking in Three Dimensional Gauge Theories
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• From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• Three-sphere free energy for classical gauge groups
• Direct derivation of "mirror" ABJ partition function
• ABJ Fractional Brane from ABJM Wilson Loop
• Exact ABJM Partition Function from TBA
• String instanton in AdS(4)xCP(3)
• Superconformal Partition Functions and Non-perturbative Topological Strings
• ABJM Wilson Loops in Arbitrary Representations
• The Partition Function of ABJ Theory
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• Interacting fermions and N=2 Chern-Simons-matter theories
• The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
• Supermatrix Models
• Eigenvalue Distributions in Matrix Models for Chern-Simons-matter Theories
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• On Large N Solution of N=3 Chern-Simons-adjoint Theories
• The topological open string wavefunction

Cited by in corpus (47)

• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Matrix models from operators and topological strings, 2
• Probing non-perturbative effects in M-theory
• Solving M-theory with the Conformal Bootstrap
• Matrix models from operators and topological strings
• Topological Strings and Quantum Spectral Problems
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• ABJM on ellipsoid and topological strings
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• Exact relations between M2-brane theories with and without Orientifolds
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• Exact Instanton Expansion of ABJM Partition Function
• Localization at large N in Chern-Simons-matter theories
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Orientifolding of the ABJ Fermi gas
• A matrix model for the latitude Wilson loop in ABJM theory
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• ABJ Wilson loops and Seiberg Duality
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Dualities and flavored indices of M2-brane SCFTs
• ABJ Quadrality
• Hanany-Witten Transition in Quantum Curves
• A Note on Instanton Effects in ABJM Theory
• Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories
• Spectral determinants and quantum theta functions
• Exact results for ABJ Wilson loops and open-closed duality
• Two-Point Functions in ABJM Matrix Model
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• Fermi gas approach to general rank theories and quantum curves
• The spectral problem of the ABJ Fermi gas
• 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
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• ABJ Theory in the Higher Spin Limit
• Duality Cascades and Parallelotopes
• 3d dualities with decoupled sectors and brane transitions
• Subleading Corrections in N=3 Gaiotto-Tomasiello Theory
• Topological phase, spin Chern-Simons theory and level rank duality on lens space