Bootstrability in defect CFT: integrated correlators and sharper bounds

Andrea Cavaglia; Nikolay Gromov; Julius Julius; Michelangelo Preti

doi:10.1007/JHEP05(2022)164

Bootstrability in defect CFT: integrated correlators and sharper bounds

Andrea Cavaglia, Nikolay Gromov, Julius Julius, Michelangelo Preti

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Abstract

We continue to develop Bootstrability — a method merging Integrability and Conformal Bootstrap to extract CFT data in integrable conformal gauge theories such as N = 4 SYM. In this paper, we consider the 1D defect CFT defined on a 12-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 λ√4π∼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.

Original language	English
Article number	164
Journal	Journal of High Energy Physics
Volume	2022
Issue number	5
DOIs	https://doi.org/10.1007/JHEP05(2022)164
Publication status	Published - 24 May 2022

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Bootstrability in defect CFT_CAVAGLIA_Publishedonline24May2022_GOLD VoR CC BYFinal published version, 3.24 MBLicence: CC BY

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title = "Bootstrability in defect CFT: integrated correlators and sharper bounds",

abstract = "We continue to develop Bootstrability — a method merging Integrability and Conformal Bootstrap to extract CFT data in integrable conformal gauge theories such as N = 4 SYM. In this paper, we consider the 1D defect CFT defined on a 12-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 {\textquoteright}t Hooft coupling in the intermediate coupling region λ√4π∼1, with the error decreasing quickly at large {\textquoteright}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.",

author = "Andrea Cavaglia and Nikolay Gromov and Julius Julius and Michelangelo Preti",

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AU - Cavaglia, Andrea

AU - Gromov, Nikolay

AU - Julius, Julius

AU - Preti, Michelangelo

PY - 2022/5/24

Y1 - 2022/5/24

N2 - We continue to develop Bootstrability — a method merging Integrability and Conformal Bootstrap to extract CFT data in integrable conformal gauge theories such as N = 4 SYM. In this paper, we consider the 1D defect CFT defined on a 12-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 λ√4π∼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.

AB - We continue to develop Bootstrability — a method merging Integrability and Conformal Bootstrap to extract CFT data in integrable conformal gauge theories such as N = 4 SYM. In this paper, we consider the 1D defect CFT defined on a 12-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 λ√4π∼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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Bootstrability in defect CFT: integrated correlators and sharper bounds

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