Abstract
In this note we investigate Graßmannian formulas for form factors of the chiral part of the stress-tensor multiplet in mathcal{N}=4 superconformal Yang-Mills theory. We present an all-n contour for the G(3, n + 2) Graßmannian integral of NMHV form factors derived from on-shell diagrams and the BCFW recursion relation. In addition, we study other G(3, n + 2) formulas obtained from the connected prescription introduced recently. We find a recursive expression for all n and study its properties. For n ≥ 6, our formula has the same recursive structure as its amplitude counterpart, making its soft behaviour manifest. Finally, we explore the connection between the two Graßmannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes.
Highlights
In addition to the on-shell momenta pi, i = 1, . . . , n satisfying p2i = 0, a form factor depends on the momentum conjugate to the position of the operator
We present an all-n contour for the G(3, n + 2) Graßmannian integral of NMHV form factors derived from on-shell diagrams and the BCFW recursion relation
We explore the connection between the two Graßmannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes
Summary
The Graßmannian formulation for Nk−2MHV form factors was introduced in [19], where a form factor top form in G(k, n + 2) was first written down. Contour prescription, and the combination of residues that compose a given form factor — originating in general from different top forms related by cyclic symmetry — was worked out case by case. We present a closed formula for the tree-level contour for NMHV form factors. This provides a systematic way of computing form factors of the chiral part of the stress-tensor operator for any n
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