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 …

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 …

A bstract We reconsider the problem of bounding higher derivative couplings in consistent
weakly coupled gravitational theories, starting from general assumptions about analyticity …

We study the constraints of crossing symmetry and unitarity in general 3D conformal field
theories. In doing so we derive new results for conformal blocks appearing in four-point …

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 …

We describe a new correspondence between four-dimensional conformal field theories with
extended supersymmetry and two-dimensional chiral algebras. The meromorphic …

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 …

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 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 …

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 …