Abstract
In this note we study the connected prescription, originally derived from Witten's twistor string theory, for tree-level form factors in ${\cal N}=4$ super-Yang-Mills theory. The construction is based on the recently proposed four-dimensional scattering equations with $n$ massless on-shell states and one off-shell state, which we expect to work for form factors of general operators. To illustrate the universality of the prescription, we propose compact formulas for super form factors with chiral stress-tensor multiplet operator, and bosonic ones with scalar operators ${\rm Tr}(\phi^m)$ for arbitrary $m$.
Highlights
JHEP12(2016)006 which are localized on the support of solutions of (1.1); for Yang-Mills amplitudes with k negative helicities in −, we have the simplest formula whose integrand is just a “ParkeTaylor” factor: An,k =
In this note we study the connected prescription, originally derived from Witten’s twistor string theory, for tree-level form factors in N = 4 super-Yang-Mills theory
Form factors provide a bridge between on-shell amplitudes and purely off-shell correlation functions, they are perfect for testing the applicability of on-shell techniques to off-shell generalizations
Summary
We present the connected formulas for the super form factors with the chiral part of the stress-tensor multiplet operator T2 in N = 4 SYM, as well as the bosonic form factor of Om (1.6), based on the chiral off-shell scattering equations (1.4). Recall that in on-shell superspace, the super form factor for the operator T2 is defined as FT2,n := δ4 P Φ1 · · · Φn | T (0) | 0 ,. D φCD are antisymmetric in A and B. T2 = T (x, θ+, u) is the chiral part of the stress-tensor multiplet operator which has the form in harmonic superspace. Its (θ+)0 component is just the scalar operator, while the (θ+) component is the chiral form of the N = 4 on-shell Lagrangian:.
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