Twistor theory—a mathematical framework that rewrites physics in the language of complex geometry—is being used to calculate what happens when particles collide inside extremely strong electromagnetic or gravitational fields. Standard methods for calculating particle interactions break down in these extreme conditions, such as those found near black holes, inside powerful laser beams, or in the curved spacetime around massive objects. Upcoming experiments will probe these regimes, from quantum electrodynamics to gravity, but theorists lack the tools to predict what they will see. This project fills that gap by using twistor theory, which the team has already shown can handle strong fields and is also linked to holography—the idea that a theory of gravity can be encoded on a lower-dimensional boundary. If successful, the research will provide concrete predictions for experiments probing strong-field physics, and supply the first detailed bottom-up data for holography in flat spacetimes. This is fundamental science with no immediate practical application, but similar mathematical breakthroughs in quantum field theory have historically underpinned technologies from semiconductors to particle accelerators.
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This proposal concerns new strategies for the study of quantum field theory (QFT) in non-perturbative settings. There are complementary experimental and theoretical incentives for pushing QFT beyond standard perturbation theory around a trivial vacuum. Upcoming experiments will probe strong field effects from quantum electrodynamics to gravity, and proposals for extending the holographic principle to asymptotically flat spacetimes require detailed knowledge of QFT beyond Minkowski space. The fundamental quantity underlying these twin imperatives is the S-matrix: the operator encoding the scattering of asymptotic states. Unfortunately, the vast majority of techniques employed in modern approaches to the S-matrix break down as soon as strong background fields or spacetime curvature are introduced. A crucial exception to this is provided by twistor theory, a framework encoding physics in terms of complex geometry. My recent work has demonstrated that twistor theory can deliver precision frontier calculations in strong field QFT and is intimately connected with approaches to asymptotically flat holography. These breakthroughs open the door on new approaches to QFT in strong backgrounds and holography in asymptotically flat spacetimes, as well as pushing twistor theory itself in novel directions. The team will deliver state-of-the-art calculations for scattering amplitudes and physical observables (both classical and quantum) in strong gauge and gravitational backgrounds including plane waves, beams, instantons and black holes, directly linked to detection targets at current or upcoming experiments. We will provide detailed bottom-up data for holography in asymptotically flat spacetimes, as well as using conformal and holomorphic field theory methods to create top-down models for the boundary dual. In parallel, we will develop new applications for twistor theory in its own right, in higher-spin theories, higher-dimensions and algebraic geometry.
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