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 -