Wilson-loop One-point Functions in ABJM Theory

Abstract

In this paper we initiate the study of correlation functions of a single trace operator and a circular supersymmetric Wilson loop in ABJM theory. The single trace operator is in the scalar sector and is an eigenstate of the planar two-loop dilatation operator. The Wilson loop is in the fundamental representation of the gauge group or a suitable (super-)group. Such correlation functions at tree level can be written as an overlap of the Bethe state corresponding to the single trace operator and a boundary state which corresponds to the Wilson loop. There are various type of supersymmetric Wilson loops in ABJM theory. We show that some of them correspond to tree-level integrable boundary states while some are not. For the tree-level integrable ones, we prove their integrability and obtain analytic formula for the overlaps. For the non-integrable ones, we give examples of non-vanishing overlaps for Bethe states which violate selection rules.

v5, 33 pages, 3 figures, minor revision

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• The type IIA Virasoro-Shapiro amplitude in AdS${}_4$ $\times$ CP${}^3$ from ABJM theory
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Three-point Functions in Aharony--Bergman--Jafferis--Maldacena Theory and Integrable Boundary States
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM
• Holographic Wilson Loop One-point Functions in ABJM Theory
• Chiral Integrable Boundary States in the SU(4) Alternating Spin Chain