A bootstrap strategy for asymptotic safety

The Hybrid Bootstrap

Finding a method to combine the numerical bootstrap with the analytic lightcone bootstrap is an important goal to advance the conformal bootstrap program. We propose a hybrid bootstrap method to do just that. The numerical and analytic bootstrap approaches are sensitive to different regions of the spectrum and complement each other. When they are effectively combined, the hybrid bootstrap enjoys the best of both worlds and the prediction for the actual CFT can be significantly improved. In this work, we discuss the general strategy to perform such a hybrid bootstrap, and we make a partial impl…

Further evidence for asymptotic safety of quantum gravity

The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using the renormalisation group, we find evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar. The extrapolation to infinite polynomial order is given, and the self-consistency of the fixed point is established using a bootstrap test. All details of our analysis are provided. We also clarify further aspects such as stability, convergence, the role of boundary conditions, and a partial degeneracy of eigenvalues. Within this setting we find strong support for…

The S-matrix Bootstrap I: QFT in AdS

We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of…

预弦理论讲座：全息关联函数与解析自举

Pre-Strings Lectures on Holographic Correlators and Analytic Bootstrap

该讲义基于预弦理论2026年学校的五次讲座，介绍了用自举策略计算全息关联函数的方法，以4d $\boldsymbol{\textrm{N}=4}$超杨-米尔斯理论为例展开，还涉及相关扩展内容。

利用光锥极限和手征代数剖析超引力子六点函数

Dissecting supergraviton six-point function with lightcone limits and chiral algebra

该研究提出结合光锥OPE与手征代数约束的引导策略，获取AdS₅×S⁵中超级引力子六点函数，可分离关联函数部分并分别确定，还能深入理解不同引导约束效力，助力计算更一般关联函数。

The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT

We compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques for computing infinite sums of SL(2,R) conformal blocks. Using these techniques, we solve the lightcone bootstrap to all orders in an asymptotic expansion in large spin, and suggest a strategy for going beyond the large spin limit. We carry out the first steps of this strategy for the 3d Ising CFT, deriving analytic approximations for the dimensions and OPE coefficients of se…