Conformal field theories have been long known to describe the fascinating universal physics
of scale invariant critical points. They describe continuous phase transitions in fluids …

This review aims to offer a pedagogical introduction to the analytic conformal bootstrap
program via a journey through selected topics. We review analytic methods which include …

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 …

A bstract We give a unified treatment of dispersive sum rules for four-point correlators in
conformal field theory. We call a sum rule “dispersive” if it has double zeros at all double …

A bstract We give a detailed account of the methods introduced in [1] to calculate
holographic four-point correlators in IIB supergravity on AdS 5× S 5. Our approach relies …

A bstract We describe in more detail our approach to the conformal bootstrap which uses the
Mellin representation of CFT d four point functions and expands them in terms of crossing …

The analytic conformal bootstrap is an array of techniques to characterize, constrain, and
solve strongly interacting quantum field theories using symmetries, causality, unitarity, and …

Abstract The critical O (N) CFT in spacetime dimensions 2< d< 4 is one of the most important
examples of a conformal field theory, with the Ising CFT at N= 1, 2⩽ d< 4, as a notable …

We propose a new approach towards analytically solving for the dynamical content of
conformal field theories (CFTs) using the bootstrap philosophy. This combines the original …

A bstract We clarify the relationships between different approaches to the conformal
bootstrap. A central role is played by the so-called extremal functionals. They are linear …