ABJM Wilson Loops in Arbitrary Representations

Abstract

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

30 pages, 1 figure; v2: references added; v3: minor corrections

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Cited by in corpus (50)

• Supersymmetric Wilson loops in N=4 super Chern-Simons-matter theory
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• Exact results on ABJ theory and the refined topological string
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• ABJ Fractional Brane from ABJM Wilson Loop
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact quantization conditions for cluster integrable systems
• Instanton Effects in Orbifold ABJM Theory
• Instanton Effects in Orientifold ABJM Theory
• Exact relations between M2-brane theories with and without Orientifolds
• Exact Instanton Expansion of ABJM Partition Function
• A profusion of $1/2$ BPS Wilson loops in $\mathcal{N}=4$ 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
• The $\mathcal{N}=4$ Schur index with Polyakov loops
• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• BPS Wilson loops in $\mathcal{N}\ge 2$ superconformal Chern-Simons-matter theories
• A matrix model for the latitude Wilson loop in ABJM theory
• ABJ Wilson loops and Seiberg Duality
• ABJ Quadrality
• Giambelli Identity in Super Chern-Simons Matrix Model
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• Hanany-Witten Transition in Quantum Curves
• Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories
• A note on multiply wound BPS Wilson loops in ABJM
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
• Matrix models for classical groups and Toeplitz$\pm$Hankel minors with applications to Chern-Simons theory and fermionic models
• Exact results for ABJ Wilson loops and open-closed duality
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• Two-Point Functions in ABJM Matrix Model
• Fermi gas approach to general rank theories and quantum curves
• (p,q)-strings probing five-brane webs
• Higher Rank ABJM Wilson Loops from Matrix Models
• Towards U(N|M) knot invariant from ABJM theory
• Spectra of Certain Holographic ABJM Wilson Loops in Higher Rank Representations
• ABJ Theory in the Higher Spin Limit
• Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
• Holographical Description of BPS Wilson Loops in Flavored ABJM Theory
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• Brane Transitions from Exceptional Groups
• Geometric transition in Non-perturbative Topological string
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• Exact results for Wilson loops in orbifold ABJM theory
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Duality Cascades and Affine Weyl Groups
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas