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 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 …

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

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 formulate a series of conjectures relating the geometry of conformal manifolds
to the spectrum of local operators in conformal field theories in d> 2 spacetime dimensions …

A bstract Distances in the conformal manifold, the space of CFTs related by marginal
deformations, can be measured in terms of the Zamolodchikov metric. Part of the CFT …

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 describe in more detail our approach to the conformal bootstrap which uses the
Mellin representation of CFT d four point functions and expands them in terms of crossing …

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