Worldsheet factorization for twistor-strings

TL;DR

This work develops a worldsheet-based framework to study multiparticle factorization in two twistor-string theories: Berkovits-Witten for $ ext{N}=4$ SYM coupled to $ ext{N}=4$ conformal supergravity and Skinner's $ ext{N}=8$ supergravity string.By enforcing a manifestly permutation-symmetric description of external states and analyzing genus-zero factorization via boundary divisors, the authors obtain a geometric, on-the-spot verification of factorization without performing Wick contractions.The paper shows that Skinner's theory yields unitary factorization in agreement with the Cachazo-Skinner tree-level formula, while Berkovits-Witten exhibits conformal-gravity–driven double-pole channels in the non-planar sector, providing a precise worldsheet interpretation of conformal gravity effects.These results illuminate structural differences from ordinary string theory, reveal how worldsheet gravity and PCOs organize factorization at genus zero, and lay groundwork for higher-genus investigations and potential links to CHY formulas and MHV-type structures.

Abstract

We study the multiparticle factorization properties of two worldsheet theories which--at tree-level--describe the scattering of massless particles in four dimensions: the Berkovits-Witten twistor-string for N=4 super-Yang-Mills coupled to N=4 conformal supergravity, and the Skinner twistor-string for N=8 supergravity. By considering these string-like theories, we can study factorization at the level of the worldsheet before any Wick contractions or integrals have been performed; this is much simpler than considering the factorization properties of the amplitudes themselves. In Skinner's twistor-string this entails the addition of worldsheet gravity as well as a formalism that represents all external states in a manifestly symmetric way, which we develop explicitly at genus zero. We confirm that the scattering amplitudes of Skinner's theory, as well as the gauge theory amplitudes for the planar sector of the Berkovits-Witten theory, factorize appropriately at genus zero. In the non-planar sector, we find behavior indicative of conformal gravity in the Berkovits-Witten twistor-string. We contrast factorization in twistor-strings with the story in ordinary string theory, and also make some remarks on higher genus factorization and disconnected prescriptions.

Figures (7)

• Figure 1: A genus three worldsheet approaches the separating divisor $\mathfrak{D}^{\mathrm{sep}}$ as the modulus $q$ approaches zero.
• Figure 2: The non-separating degeneration reduces the genus of the worldsheet by one.
• Figure 3: Near the boundary divisor, $\mathcal{V}_{a}$ and $\mathcal{V}_{b}$ are inserted at opposite ends of a long tube.
• Figure 4: Worldsheet factorization in the planar limit of the Berkovits-Witten twistor-string at 8-points.
• Figure 5: The puncture operators effectively cut the single trace (dotted lines) into a double trace (solid lines) as we approach the boundary divisor.