Over the past 15 years, the numerical conformal bootstrap has become an indispensable
tool for studying strongly coupled conformal field theories in various dimensions. Reviewed …

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 …

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 study the torus partition functions of free bosonic CFTs in two dimensions.
Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the …

Using the numerical modular bootstrap, we constrain the space of 1+ 1 d conformal field
theories (CFTs) with a finite noninvertible global symmetry described by a fusion category C …

A bstract It is a long-standing conjecture that any CFT with a large central charge and a large
gap∆ gap in the spectrum of higher-spin single-trace operators must be dual to a local …

A bstract A key issue in both the field of quantum chaos and quantum gravity is an effective
description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum …

A bstract Recent progress in AdS/CFT has provided a good understanding of how the bulk
spacetime is encoded in the entanglement structure of the boundary CFT. However, little is …

A bstract We introduce a framework for quantifying random matrix behavior of 2d CFTs and
AdS 3 quantum gravity. We present a 2d CFT trace formula, precisely analogous to the …

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 …