A duality for the S matrix

Abstract

We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "leading singularities" of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely determine the full amplitudes at tree level and 1-loop, and are conjectured to do so at all loop orders. The scattering amplitude for n particles in the sector with k negative helicity gluons is associated with a simple integral over the space of k planes in n dimensions, with the action of parity and cyclic symmetries manifest. The residues of the integrand compute a basis for the leading singularities. A given leading singularity is associated with a particular choice of integration contour, which we explicitly identify at tree level and 1-loop for all NMHV amplitudes as well as the 8 particle N 2 MHV amplitude. We also identify a number of 2-loop leading singularities for up to 8 particles. There are a large number of relations among residues which follow from the multi-variable generalization of Cauchy's theorem known as the "global residue theorem". These relations imply highly non-trivial identities guaranteeing the equivalence of many different representations of the same amplitude. They also enforce the cancellation of non-local poles as well as consistent infrared structure at loop level. Our conjecture connects the physics of scattering amplitudes to a particular subvariety in a Grassmannian; space-time locality is reflected in the topological properties of this 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…”

From six to four and more: massless and massive maximal super Yang-Mills amplitudes in 6d and 4d and their hidden symmetries

“…In contrast to the earlier Berends-Giele off-shell recursion relations [14], the BCFW relation uses only on-shell lower-point amplitudes, evaluated at complex, shifted momenta. The BCFW recursion relation is easily generalizable to an on-shell recursion for superamplitudes, as was done for N = 4 SYM in [15] (see also [16]). In fact the knowledge of the dual superconformal invariance of superamplitudes motivates an ansatz in terms of dual conformal invariants.…”

Constructing amplitudes from their soft limits

“…A recent advancement in this area due to Arkani-Hamed, et al, is a method called inverse soft which attempts to construct amplitudes from their soft limits alone [14][15][16]. Inverse soft was motivated by…”