Wilson-loop one-point functions in ABJM theory

• Published in: The journal of high energy physics Vol. 2023; no. 9; pp. 47 - 32
• Main Authors: Jiang, Yunfeng, Wu, Jun-Bao, Yang, Peihe
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 08.09.2023; Springer Nature B.V; SpringerOpen
• Subjects: Bethe Ansatz; Boundary conditions; Chern-Simons Theories; Classical and Quantum Gravitation; Correlation; Eigenvectors; Elementary Particles; High energy physics; Mathematical analysis; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetric Gauge Theory; Supersymmetry; t Hooft and Polyakov loops; Wilson; Wilson; t Hooft and Polyakov loops; Bethe Ansatz; Chern-Simons Theories; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2023)047

A bstract 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.