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 Effective field theories (EFT) parameterize the long-distance effects of short-
distance dynamics whose details may or may not be known. Previous work showed that EFT …

We find the complete set of conditions satisfied by the forward 2→ 2 scattering amplitude in
unitary and causal theories. These are based on an infinite set of energy dependent …

A bstract Celestial amplitudes represent 4D scattering of particles in boost, rather than the
usual energy-momentum, eigenstates and hence are sensitive to both UV and IR physics …

The S-matrix Bootstrap originated on the idea that the S-matrix might be fully constrained by
global symmetries, crossing, unitarity, and analyticity without relying on an underlying …

A bstract We revisit from a modern bootstrap perspective the longstanding problem of
solving QCD in the large N limit. We derive universal bounds on the effective field theory of …

Fundamental principles of local quantum field theory or of quantum gravity can enforce
consistency requirements on the space of consistent low-energy effective field theories. We …

A bstract The wavefunction in quantum field theory is an invaluable tool for tackling a variety
of problems, including probing the interior of Minkowski spacetime and modelling boundary …

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 …

We use the S-matrix bootstrap to carve out the space of unitary, crossing symmetric and
supersymmetric graviton scattering amplitudes in ten dimensions. We focus on the leading …