Dual superconformal invariance, momentum twistors and Grassmannians

Abstract

Dual superconformal invariance has recently emerged as a hidden symmetry of planar scattering amplitudes in N = 4 super Yang-Mills theory. This symmetry can be made manifest by expressing amplitudes in terms of 'momentum twistors', as opposed to the usual twistors that make the ordinary superconformal properties manifest. The relation between momentum twistors and on-shell momenta is algebraic, so the translation procedure does not rely on any choice of space-time signature. We show that tree amplitudes and box coefficients are succinctly generated by integration of holomorphic δ-functions in momentum twistors over cycles in a Grassmannian. This is analogous to, although distinct from, recent results obtained by Arkani-Hamed et al. in ordinary twistor space. We also make contact with Hodges' polyhedral representation of NMHV amplitudes in momentum twistor space.

The super-correlator/super-amplitude duality: Part I

“…, n − 4) of the odd variables. This Grassmann structure is very similar to that of the super-amplitude rewritten in momentum super-twistor space [42][43][44]. We claim that in the light-cone limit such super-correlators are dual to super-amplitudes, as the direct supersymmetric generalization of the bosonic duality (1.5): 8) after the appropriate identification of the variables on both sides.…”

“…It proves convenient to introduce yet another set of dual variables, the so-called momentum supertwistors [42][43][44]:…”

“…The R invariants can be rewritten in terms of the so-called momentum super-twistors [42][43][44]. The bosonic momentum twistor is defined by…”

“…In [44] the R invariants (5.2) were rewritten in terms of momentum supertwistors with 5 labels r, s − 1, s, t − 1, t instead of the 3 labels r, s, t in (5.2):…”

Gravity on-shell diagrams

“…This space is known as the Grassmannian G(k, n). Using these auxiliary variables, momentum conservation is enforced geometrically [32][33][34] via the following set of delta functions (similar relations hold in twistor and momentum twistor spaces),…”