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 …

A bstract We make precise determinations of the leading scaling dimensions and operator
product expansion (OPE) coefficients in the 3d Ising, O (2), and O (3) models from the …

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 …

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 propose a strategy to study massive Quantum Field Theory (QFT) using
conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study …

We use the S-matrix bootstrap to carve out the space of unitary, crossing symmetric and
supersymmetric graviton scattering amplitudes in ten dimensions. We focus on the leading …

A bstract Every four-dimensional\(\mathcal {N}= 2\) superconformal field theory comes
equipped with an intricate algebraic invariant, the associated vertex operator algebra. The …

A bstract We introduce a large class of conformally-covariant differential operators and a
crossing equation that they obey. Together, these tools dramatically simplify calculations …

Abstract Six-dimensional (6D) superconformal field theories (SCFTs) occupy a central place
in the study of quantum field theories encountered in high energy theory. This article reviews …