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 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 …

A remarkable yet mysterious property of black holes is that their entropy is proportional to the
horizon area. This area law inspired the holographic principle, which was later realized …

A bstract We prove a conjectured lower bound on< T__ (x)> ψ in any state ψ of a CFT on
Minkowski space, dubbed the Quantum Null Energy Condition (QNEC). The bound is given …

A bstract We use the numerical bootstrap to study conformal line defects with O (2) global
symmetry. Our results are very general and capture in particular conformal line defects …

A bstract We consider the structure of current and stress tensor two-point functions in
conformal field theory with a boundary. The main result of this paper is a relation between a …

A bstract I study the two-dimensional defects of the d dimensional critical O (N) model and
the defect RG flows between them. By combining the ϵ-expansion around d= 4 and d= 6 as …

A bstract We study the constraints of superconformal symmetry on codimension two defects
in four-dimensional superconformal field theories. We show that the one-point function of the …

A bstract For a single free scalar field in d≥ 2 dimensions, almost all the unitary conformal
defects must be 'trivial'in the sense that they cannot hold interesting dynamics. The only …

A bstract We study the spectrum of local operators living on a defect in a generic conformal
field theory, and their coupling to the local bulk operators. We establish the existence of …