Extending single-minus amplitudes to gravitons

Source: OpenAI Blog

Overview

We have released a new preprint that extends recent results obtained for gluons to the gravitational setting. The work demonstrates that a class of graviton interactions, previously assumed to vanish, can in fact arise under well‑defined kinematic conditions. The preprint is available here.

The paper, “Single-minus graviton tree amplitudes are nonzero,” is authored by Alfredo Guevara (Institute for Advanced Study), Alexandru Lupsasca (Vanderbilt University and OpenAI), David Skinner (University of Cambridge), Andrew Strominger (Harvard University), and Kevin Weil (OpenAI) on behalf of OpenAI.

Background on Scattering Amplitudes

Scattering amplitudes are mathematical objects that encode the probabilities of particle interactions. Rather than summing over many intermediate Feynman diagrams, amplitudes provide a compact description of the observable outcomes. Over the past several decades, researchers have uncovered surprising simplicity and hidden mathematical structures in amplitudes that are not evident from traditional calculations.

Single-minus Graviton Tree Amplitudes

The preprint focuses on single-minus amplitudes for gravitons, where one external graviton carries negative helicity and the remaining gravitons carry positive helicity. Standard textbook arguments predict that such tree‑level amplitudes should vanish. However, this conclusion relies on the assumption of generic particle momenta.

When the external momenta satisfy a special alignment known as the half‑collinear regime, the usual vanishing argument no longer applies. In this regime the amplitudes become non‑zero distributions supported on a restricted region of momentum space. Explicit formulas for these amplitudes are derived, showing that they follow from symmetry principles and recursion relations that build complex interactions from simpler ones.

Derivation and Techniques

The derivation combines several established tools in amplitude theory:

• Recursion relations that iteratively construct many‑particle interactions from lower‑point building blocks.
• Symmetry constraints that restrict the allowed form of the result.
• The directed matrix‑tree theorem, employed to obtain compact expressions for the amplitudes.

The final formulas were verified analytically and checked for consistency with known physical limits. They also satisfy an infinite‑dimensional “(w!-!(1+\infty))” symmetry first studied by Roger Penrose in the context of classical gravity.

Symmetry Implications

The non‑vanishing single‑minus amplitudes realize the infinite‑dimensional (w!-!(1+\infty)) symmetry. This powerful symmetry, discovered by Penrose half a century ago, is expected to play a central role in the quantization of the gravitational field. The present work shows how this symmetry acts on gravitons in the simplest possible context.

AI‑Assisted Contribution

The earlier gluon result demonstrated that a previously neglected helicity configuration could produce non‑zero amplitudes under special conditions. After that work was completed, the gluon paper was provided to GPT‑5.2 Pro as context. Using it as a reference, the model was asked to construct the corresponding amplitudes in quantum gravity—an extension that would have required considerable time for human authors.

GPT‑5.2 Pro solved the problem using the directed matrix‑tree theorem and produced an excellent preliminary draft of the paper. A transcript of the initial exchange is available here.

The project highlights a shift in the research workflow: the majority of effort was spent on verification, consistency checks, and formal write‑up rather than on generating the initial conjectures.

Future Directions

Further extensions of these results are under investigation. Together with the earlier gluon work, this preprint contributes to an ongoing effort to understand how AI‑assisted reasoning can participate in theoretical research while maintaining conventional standards of mathematical verification and scientific rigor.