Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-12-03
Physics
High Energy Physics
High Energy Physics - Theory
50 pages, 20 figures. Section 2.5 extended, errors in 5.2 corrected, new section 5.3 inserted, references added. In all, 5 new
Scientific paper
We derive a systematic procedure for obtaining an explicit, L-loop leading singularities of planar N=4 super Yang-Mills scattering amplitudes in twistor space directly from their momentum space channel diagrams. 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 formulae 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 N^{k-2}MHV amplitudes may be mapped into the Grassmannian G(k,n). Restricting to a leading singularity, the image of this map is a 2(n-2)-dimensional subcycle of G(k,n) of exactly the type found from the Grassmannian residue formula of Arkani-Hamed, Cachazo, Cheung and Kaplan. Based on this correspondence and the Grassmannian conjecture, we deduce restrictions on the possible leading singularities of multi-loop N^pMHV amplitudes. In particular, we argue that no new leading singularities can arise beyond 3p loops.
Bullimore Mathew
Mason Lionel
Skinner David
No associations
LandOfFree
Twistor-Strings, Grassmannians and Leading Singularities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Twistor-Strings, Grassmannians and Leading Singularities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Twistor-Strings, Grassmannians and Leading Singularities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-419704