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 derive a refined version of the Affleck-Ludwig-Cardy formula for a 1+ 1 D conformal field
theory, which controls the asymptotic density of high energy states on an interval …

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 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 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 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 …

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

A bstract We consider the triality fusion category discovered in the c= 1 Kosterlitz-Thouless
theory [1]. We analyze this fusion category using the tools from the group theoretical fusion …

We explore constraints on (1+ 1) d unitary conformal field theory with an internal ZN global
symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the …

A bstract We perform a comprehensive analysis of the symmetry-resolved (SR)
entanglement entropy (EE) for one single interval in the ground state of a 1+ 1D conformal …