Bootstrability in defect CFT: integrated correlators and sharper bounds

TY - JOUR

T1 - Bootstrability in defect CFT

T2 - integrated correlators and sharper bounds

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.

UR - http://www.scopus.com/inward/record.url?scp=85130753026&partnerID=8YFLogxK

U2 - 10.1007/JHEP05(2022)164

DO - 10.1007/JHEP05(2022)164

M3 - Article

SN - 1126-6708

VL - 2022

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 5

M1 - 164

ER -