ABJ Fractional Brane from ABJM Wilson Loop

Abstract

We present a new Fermi gas formalism for the ABJ matrix model. This formulation identifies the effect of the fractional M2-brane in the ABJ matrix model as that of a composite Wilson loop operator in the corresponding ABJM matrix model. Using this formalism, we study the phase part of the ABJ partition function numerically and find a simple expression for it. We further compute a few exact values of the partition function at some coupling constants. Fitting these exact values against the expected form of the grand potential, we can determine the grand potential with exact coefficients. The results at various coupling constants enable us to conjecture an explicit form of the grand potential for general coupling constants. The part of the conjectured grand potential from the perturbative sum, worldsheet instantons and bound states is regarded as a natural generalization of that in the ABJM matrix model, though the membrane instanton part contains a new contribution.

28 pages, 5 eps figures, v3: typos corrected and references added, version to appear in JHEP

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Cited by in corpus (50)

• Probing non-perturbative effects in M-theory
• Exact results on ABJ theory and the refined topological string
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• Instanton effects in ABJM theory with general R-charge assignments
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• 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
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
• 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
• Instanton Effects in Orientifold ABJM Theory
• Exact relations between M2-brane theories with and without Orientifolds
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Exact Instanton Expansion of ABJM Partition Function
• Localization at large N in Chern-Simons-matter theories
• 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
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Orientifolding of the ABJ Fermi gas
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• Complete factorization in minimal N=4 Chern-Simons-matter theory
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• A matrix model for the latitude Wilson loop in ABJM theory
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• ABJ Quadrality
• Giambelli Identity in Super Chern-Simons Matrix Model
• Hanany-Witten Transition in Quantum Curves
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
• Localization and Duality for ABJM Latitude Wilson Loops
• Exact results for ABJ Wilson loops and open-closed duality
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• Fermi gas approach to general rank theories and quantum curves
• Two-Point Functions in ABJM Matrix Model
• SU(N) q-Toda equations from mass deformed ABJM theory
• Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual
• Non-perturbative Tests of Duality Cascades in Three Dimensional Supersymmetric Gauge Theories
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• ABJ Theory in the Higher Spin Limit
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Duality Cascades and Affine Weyl Groups
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• Duality Cascades and Parallelotopes
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• Topological phase, spin Chern-Simons theory and level rank duality on lens space
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas