Twistor Strings for N=8 Supergravity

TL;DR

This work constructs a twistor-string worldsheet theory for ${\mathcal{N}}=8$ supergravity, showing anomaly cancellation only occurs at ${\mathcal{N}}=8$ and deriving an S-matrix from worldsheet correlators via the Penrose transform. In flat space, the tree-level gravity amplitudes arise from correlators that reproduce Hodges’ determinant structure, with the worldsheet Hodges matrix ${\mathbb{H}}$ and its conjugate ${\mathbb{H}}^{\vee}$ encoding the full amplitude data. The formalism unifies fixed and integrated vertex operators into a single CPT-invariant ${\mathcal{N}}=8$ multiplet and incorporates picture-changing operators to saturate moduli, yielding a complete tree-level S-matrix ${\mathcal{M}}_{n,k}$ when summed over degrees. The approach also admits AdS$_4$ backgrounds (via a nondegenerate infinity twistor) and suggests avenues toward higher-genus amplitudes, boundary correlators, and deeper links with twistor actions for gravity. Overall, the paper provides a coherent twistor-string framework that explains the Hodges determinant structure of ${\mathcal{N}}=8$ supergravity amplitudes and opens paths to non-flat backgrounds and loop-level generalizations.

Abstract

This paper presents a worldsheet theory describing holomorphic maps to twistor space with N fermionic directions. The theory is anomaly free when N=8. Via the Penrose transform, the vertex operators correspond to an N=8 Einstein supergravity multiplet. In the first instance, the theory describes gauged supergravity in AdS_4. Upon taking the flat space, ungauged limit, the complete classical S-matrix is recovered from worldsheet correlation functions.