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Twistor-strings, Grassmannians and leading singularities

Bullimore, Mathew; Mason, Lionel; Skinner, David

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Lionel Mason

David Skinner


We derive a systematic procedure for obtaining explicit, ℓ-loop leading singularities of planar N = 4 super Yang-Mills scattering amplitudes in twistor space directly from their momentum space channel diagram. The expressions are given as integrals over the moduli of connected, nodal curves in twistor space whose degree and genus matches expectations from twistor-string theory. We propose that a twistor-string theory for pure N = 4 super Yang-Mills — if it exists — is determined by the condition that these leading singularity formulæ arise as residues when an unphysical contour for the path integral is used, by analogy with the momentum space leading singularity conjecture. We go on to show that the genus g twistor-string moduli space for g-loop Nk−2MHV amplitudes may be mapped into the Grassmannian G(k, n). For a leading singularity, the image of this map is a 2(n − 2)-dimensional subcycle of G(k, n) and, when ‘primitive’, it is of exactly the type found from the Grassmannian residue formula of Arkani-Hamed, Cachazo, Cheung & Kaplan. Based on this correspondence and the Grassmannian conjecture, we deduce restrictions on the possible leading singularities of multi-loop N p MHV amplitudes. In particular, we argue that no new leading singularities can arise beyond 3p loops.


Bullimore, M., Mason, L., & Skinner, D. (2010). Twistor-strings, Grassmannians and leading singularities. Journal of High Energy Physics, 2010(03), Article 070.

Journal Article Type Article
Acceptance Date Jan 28, 2010
Online Publication Date Mar 13, 2010
Publication Date Mar 13, 2010
Deposit Date Jun 7, 2018
Publicly Available Date Jul 2, 2018
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2010
Issue 03
Article Number 070


Accepted Journal Article (1.5 Mb)

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