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

We analyze constraints from perturbative unitarity and crossing on the leading contributions
of higher-dimension operators to the four-graviton amplitude in four spacetime dimensions …

A bstract It is a long-standing conjecture that any CFT with a large central charge and a large
gap∆ gap in the spectrum of higher-spin single-trace operators must be dual to a local …

A bstract We give a unified treatment of dispersive sum rules for four-point correlators in
conformal field theory. We call a sum rule “dispersive” if it has double zeros at all double …

In this paper we take the first steps towards bridging the gap between the conformal and
cosmological bootstrap programs. We present a simple general relation between tree-level …

We study the analytic properties of tree-level wavefunction coefficients in quasi-de Sitter
space. We focus on theories which spontaneously break dS boost symmetries and can …

A bstract We revisit analytical methods for constraining the nonperturbative S-matrix of
unitary, relativistic, gapped theories in d≥ 3 spacetime dimensions. We assume extended …

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

A bstract We derive the Cutkosky rules for conformal field theories (CFTs) at weak and
strong coupling. These rules give a simple, diagrammatic method to compute the double …