Abstract
We continue to develop Bootstrability — a method merging Integrability and Conformal Bootstrap to extract CFT data in integrable conformal gauge theories such as \( \mathcal{N} \) = 4 SYM. In this paper, we consider the 1D defect CFT defined on a \( \frac{1}{2} \)-BPS Wilson line in the theory, whose non-perturbative spectrum is governed by the Quantum Spectral Curve (QSC). In addition, we use that the deformed setup of a cusped Wilson line is also controlled by the QSC. In terms of the defect CFT, this translates into two nontrivial relations connecting integrated 4-point correlators to cusp spectral data, such as the Bremsstrahlung and Curvature functions — known analytically from the QSC. Combining these new constraints and the spectrum of the 10 lowest-lying states with the Numerical Conformal Bootstrap, we obtain very sharp rigorous numerical bounds for the structure constant of the first non-protected state, giving this observable with seven digits precision for the ’t Hooft coupling in the intermediate coupling region \( \frac{\sqrt{\lambda }}{4\pi}\sim 1 \), with the error decreasing quickly at large ’t Hooft coupling. Furthermore, for the same structure constant we obtain a 4-loop analytic result at weak coupling. We also present results for excited states.
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Cavaglià, A., Gromov, N., Julius, J. et al. Bootstrability in defect CFT: integrated correlators and sharper bounds. J. High Energ. Phys. 2022, 164 (2022). https://doi.org/10.1007/JHEP05(2022)164
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DOI: https://doi.org/10.1007/JHEP05(2022)164