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 …

These notes are from courses given at TASI and the Advanced Strings School in summer
2015. Starting from principles of quantum field theory and the assumption of a traceless …

We consider line defects in d-dimensional conformal field theories (CFTs). The ambient CFT
places nontrivial constraints on renormalization group (RG) flows on such line defects. We …

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 use the conformal bootstrap to perform a precision study of the operator spectrum of the
critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central …

A bstract We introduce SDPB: an open-source, parallelized, arbitrary-precision semidefinite
program solver, designed for the conformal bootstrap. SDPB significantly outperforms less …

A bstract We discuss consequences of the breaking of conformal symmetry by a flat or
spherical extended operator. We adapt the embedding formalism to the study of correlation …

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 consider several aspects of unitary higher-dimensional conformal field theories
(CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep …