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 …

Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos
in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally …

A bstract We argue that every CFT contains light-ray operators labeled by a continuous spin
J. When J is a positive integer, light-ray operators become integrals of local operators over a …

A bstract We develop new tools for isolating CFTs using the numerical bootstrap. A “cutting
surface” algorithm for scanning OPE coefficients makes it possible to find islands in high …

A bstract Equilibrium finite temperature observables of a CFT can be described by a local
effective action for background fields—a “thermal effective action”. This effective action …

A bstract We show that holographic thermal two-sided two-point correlators take the form of
a product over quasi-normal modes (QNMs). Due to this fact, the two-point function admits a …

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

We present an exact formula for the thermal scalar two-point function in four-dimensional
holographic conformal field theories. The problem of finding it reduces to the analysis of the …

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 …