Exact Results in ABJM Theory from Topological Strings

Abstract

Recently, Kapustin, Willett and Yaakov have found, by using localization techniques, that vacuum expectation values of Wilson loops in ABJM theory can be calculated with a matrix model. We show that this matrix model is closely related to Chern-Simons theory on a lens space with a gauge supergroup. This theory has a topological string large N dual, and this makes possible to solve the matrix model exactly in the large N expansion. In particular, we find the exact expression for the vacuum expectation value of a 1/6 BPS Wilson loop in the ABJM theory, as a function of the 't Hooft parameters, and in the planar limit. This expression gives an exact interpolating function between the weak and the strong coupling regimes. The behavior at strong coupling is in precise agreement with the prediction of the AdS string dual. We also give explicit results for the 1/2 BPS Wilson loop recently constructed by Drukker and Trancanelli

18 pages, two figures, small misprints corrected and references added, final version to appear in JHEP

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Cited by in corpus (147)

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• Multi-Matrix Models and Tri-Sasaki Einstein Spaces
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• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
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• Exact results on ABJ theory and the refined topological string
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• The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories
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• ABJM Wilson Loops in Arbitrary Representations
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• The Partition Function of ABJ Theory
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• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
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• Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
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• Virasoro constraints revisited
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