Pre-Strings Lectures on Holographic Correlators and Analytic Bootstrap

Abstract

Over the past decade, the bootstrap strategy has transformed the computation of holographic correlators and revealed structures suggesting an emerging scattering amplitude program in AdS. These notes, which are an extended version of the five lectures delivered at the Pre-Strings 2026 School, give a pedagogical introduction and synthesis of these developments. We start with a quick reminder of the essentials of CFT and a brief review of AdS perturbation theory. We then demonstrate in detail the bootstrap strategy for computing holographic correlators in the canonical example 4d $\mathcal{N}=4$ super Yang-Mills theory, at the level of four-point functions and in the regime dual to classical Type IIB supergravity. Several extensions, including higher-point functions, quantum corrections and stringy corrections, are discussed at varying levels of detail. We also explain how the bootstrap strategy can be extended to holographic CFTs with conformal defects, covering a diverse array of different setups.