Scattering amplitudes in strong background fields provide an arena where perturbative and non-perturbative physics meet, with important applications ranging from laser physics to black holes, but their study is hampered by the cumbersome nature of QFT in the background field formalism. In this talk, I will try to convince you that strong-field scattering amplitudes contain a wealth of physical information which cannot be obtained with standard perturbative techniques, ranging from all-order classical observables to constraints on exact solutions. Furthermore, I will discuss how in chiral strong fields, remarkable progress is possible using methods based on twistor theory.

Usually, scattering amplitudes in quantum field theory are computed perturbatively around a trivial background, but there are many reasons to be interested in non-trivial (or 'strong') background fields. These range from laser physics and QCD processes near heavy ion collisions to gravitational waves, conformal field theories and cosmology. Strong backgrounds also give us a way to test the robustness of new structures which have been discovered in scattering amplitudes. I will discuss perturbative Yang-Mills theory on a particularly simple (but important) background known as a plane wave, and consider a very basic observable: the scattering amplitude for a gluon to flip helicity as it crosses the background. This 'helicity flip' amplitude is a loop effect, and the leading result for Yang-Mills (and QCD) can be expressed compactly using a background-dressed version of the spinor helicity formalism (a method for freely specifying on-shell kinematics). Time permitting, I may also make some remarks about higher-point gluon amplitudes in the plane wave background, or the version of this story for gravity.

There are many reasons to consider perturbative QFT around curved backgrounds, but it is often difficult to perform explicit computations in these settings. Progress in the study of scattering amplitudes (around a trivial background) suggests alternative perspectives to space-time Lagrangians and Feynman rules which could enable progress in the study of scattering on curved backgrounds. I will discuss one such alternative, known as double copy, with a particular focus on gluon and graviton scattering around non-linear plane wave backgrounds

In recent years, there has been significant process in the study of perturbative field theory scattering amplitudes using certain 2d chiral, first-order CFTs known as 'ambitwistor string theories.' After a brief review of the ambitwistor setup, I will introduce a related family of 2d CFTs, which can be viewed as constrained ambitwistor strings. These new models describe holomorphic maps from the Riemann sphere to the projective null cone in D-dimensional Minkowski space. This target space is the natural setting to describe field theories with (classical) conformal invariance in (D-2)-dimensions. Killing the anomalies associated with these models fixes critical dimensions for which three well-known space-time field theories (bi-adjoint cubic scalar, gauge theory, gravity) are conformal. Furthermore, the spectrum of each model contains all single field insertions, along with their conformal descendants, of the correct scaling dimension. Time permitting, I will also outline how the space-time 3-point functions can be obtained from the 3-point correlators on the Riemann sphere.