Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds

TL;DR

This paper advances the Bootstrability method by integrating integrability and conformal bootstrap techniques to derive precise bounds on defect CFT data in N=4 SYM, utilizing Quantum Spectral Curve constraints.

Contribution

It introduces new relations connecting integrated correlators to spectral data, improving bounds on structure constants and providing analytic results at weak coupling.

Findings

Achieved seven-digit precision for the structure constant at intermediate coupling.

Derived a four-loop analytic expression for the structure constant at weak coupling.

Obtained sharp numerical bounds for excited states in the defect CFT.

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.