Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$

Abstract

We study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT${}_1$ with SU$(1,1|3)$ superconformal symmetry defined on the 1/2-BPS Wilson line. The relevant insertions belong to the short supermultiplet containing the displacement operator and correspond to fluctuations of the dual fundamental string in AdS${}_4\times \mathbb{C}{\text{P}}^3$ ending on the line at the boundary. We use superspace techniques to represent the displacement supermultiplet and we show that superconformal symmetry determines the four-point correlators of its components in terms of a single function of the one-dimensional cross-ratio. Such function is highly constrained by crossing and internal consistency, allowing us to use an analytical bootstrap approach to find the first subleading correction at strong coupling. Finally, we use AdS/CFT to compute the same four-point functions through tree-level AdS${}_2$ Witten diagrams, producing a result that is perfectly consistent with the bootstrap solution.

arXiv comment50 pages, 2 figures. v2: one footnote and one reference added, it matches the published version v3: further references added

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• Broken global symmetries and defect conformal manifolds
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• Wilson loops at large $N$ and the quantum M2 brane
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
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• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Notes on hyperloops in N=4 Chern-Simons-matter theories
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Mellin amplitudes for 1$d$ CFT
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• The topological line of ABJ(M) theory
• On three-point functions in ABJM and the latitude Wilson loop
• 1/3 BPS loops and defect CFTs in ABJM theory
• Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory
• Conformal and non-conformal hyperloop deformations of the 1/2 BPS circle
• Notes on $n$-point Witten diagrams in AdS${}_2$
• Conformal line defects at finite temperature
• Interpolating Boundary Conditions on $Ad{S}_2$
• On the abundance of supersymmetric strings in $Ad{S}_3\times S^3\times S^3\times S^1$ describing BPS line operators
• Interpolating Bremsstrahlung function in ABJM
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• 1d Conformal Field Theory and Dispersion Relations
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Universal sectors in superconformal defects
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM
• Boundary bound states and integrable Wilson loops in ABJM
• A network of hyperloops
• Holographic Wilson Loop One-point Functions in ABJM Theory