Abstract
We propose a connected prescription formula in twistor space for all tree-level form factors of the stress tensor multiplet operator in $\mathcal{N}=4$ super Yang-Mills, which is a generalisation of the expression of Roiban, Spradlin and Volovich for superamplitudes. By introducing link variables, we show that our formula is identical to the recently proposed four-dimensional scattering equations for form factors. Similarly to the case of amplitudes, the link representation of form factors is shown to be directly related to BCFW recursion relations, and is considerably more tractable than the scattering equations. We also discuss how our results are related to a recent Grassmannian formulation of form factors, and comment on a possible derivation of our formula from ambitwistor strings.
Highlights
JHEP11(2016)143 operator O to the vacuum and projecting the result onto an n-particle state of on-shell particles with momenta pi obeying q := p1 + · · · + pn
We propose a connected prescription formula in twistor space for all tree-level form factors of the stress tensor multiplet operator in N = 4 super Yang-Mills, which is a generalisation of the expression of Roiban, Spradlin and Volovich for superamplitudes
We show that our formula is identical to the recently proposed four-dimensional scattering equations for form factors
Summary
We begin by describing the main ingredients of the connected formula for form factors. The momentum and supermomentum carried by the form factor will be q := λxλx + λyλy and γ := λxηx + λyηy, respectively In twistor space, this amounts to introducing two extra super-twistors Zx and Zy. 2. We propose that all form factors of the supersymmetric stress tensor multiplet operator in N = 4 SYM are described in twistor space by the following simple generalisation of the. A convenient choice when working with, say, component gluon amplitudes is to assign gluons of negative (positive) helicity to the first (second) group, with the fictitious particles x and y being included in the second set This parallels the assignments made in [14] for the non-supersymmetric scattering equations for form factors, where these two particles are treated as gluons of positive helicity. By performing in reverse the same steps of this proof, one can derive the connected prescription for form factors (2.2) from the scattering equations.
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