In this lecture note, we give a basic introduction to the rapidly develo** concepts of
generalized symmetries, from the perspectives of both high energy physics and condensed …

A bstract We show that color-kinematics duality is a manifest property of the equations of
motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this …

We show that the BRST Lagrangian double copy construction of supergravity as the
'square'of Yang–Mills theory finds a natural interpretation in terms of homotopy algebras. We …

A bstract We systematically explore the space of scalar effective field theories (EFTs)
consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT …

These lectures are a brief introduction to scattering amplitudes. We begin with a review of
basic kinematical concepts like the spinor helicity formalism, followed by a tutorial on …

We derive the first ever on-shell recursion relations applicable to effective field theories.
Based solely on factorization and the soft behavior of amplitudes, these recursion relations …

A bstract We derive a universal soft theorem for every scattering amplitude with at least one
massless particle in an arbitrary theory of scalars. Our results follow from the geometry of …

A bstract We define a perturbatively calculable quantity—the on-shell correlator—which
furnishes a unified description of particle dynamics in curved spacetime. Specializing to the …

We propose a map** between geometry and kinematics that implies the classical
equivalence of any theory of massless bosons—including spin and exhibiting arbitrary …

A bstract The soft bootstrap is an on-shell method to constrain the landscape of effective field
theories (EFTs) of massless particles via the consistency of the low-energy S-matrix. Given …