A Note on Twistor Gravity Amplitudes

TL;DR

This note investigates whether gravity amplitudes admit twistor-space localization analogous to Witten’s twistor-string picture for Yang-Mills theory. It shows the simplest nontrivial googly gravity amplitude localizes on a connected degree-2 twistor curve, with the twistor transform involving derivatives of delta functions, indicating non-holomorphic support. The authors also test a completely disconnected MHV decomposition and find it fails for gravity in several helicity configurations, with the googly case revealing a non-holomorphic 4-vertex that spoils covariance in naive constructions. Together, these results suggest gravity may require a different twistor-string framework or additional ingredients to realize a full localization picture and practical MHV-like expansions.

Abstract

In a recent paper, Witten proposed a surprising connection between perturbative gauge theory and a certain topological model in twistor space. In particular, he showed that gluon amplitudes are localized on holomorphic curves. In this note we present some preliminary considerations on the possibility of having a similar localization for gravity amplitudes.

Figures (6)

• Figure 1: Two disconnected configurations contributing to $\mathcal{M}_n(1+,2-,\ldots,n-)$.
• Figure 2: The $(+,-,-)$ graviton vertex.
• Figure 3: The MHV diagrams contributing to the $\mathcal{M}(1+,2-,3-,4-)$ graviton amplitude.
• Figure 4: Two of the fifteen MHV diagrams contributing to the $\mathcal{M}(1+,2-,3-,4-,5-)$ graviton amplitude.
• Figure 5: The $(+,+,-,-)$ graviton vertex.