Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve

Abstract

We study the anomalous dimension of the cusped Maldacena-Wilson line in planar $\mathcal{N}=4$ Yang-Mills theory with scalar insertions using the Quantum Spectral Curve (QSC) method. In the straight line limit we interpret the excited states of the QSC as insertions of scalar operators coupled to the line. Such insertions were recently intensively studied in the context of the one-dimensional defect CFT. We compute a five-loop perturbative result analytically at weak coupling and the first four orders in the $1/\sqrt{\lambda }$ expansion at strong coupling, confirming all previous analytic results. In addition, we find the non-perturbative spectrum numerically and show that it interpolates smoothly between the weak and strong coupling predictions.

arXiv comment27 pages, 5 figures, 1 table

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• Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$
• Broken global symmetries and defect conformal manifolds
• Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Mellin amplitudes for 1$d$ CFT
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Conformal line defects at finite temperature
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
• Higher order RG flow on the Wilson line in $\mathcal{N}=4$ SYM
• Beyond AdS${}_2$/dCFT${}_1$: Insertions in Two Wilson Loops
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM
• Holographic Wilson Loop One-point Functions in ABJM Theory