Abstract
We study the multiparticle factorization properties of two worldsheet theories which--at tree-level--describe the scattering of massless particles in four dimensions: the Berkovits-Witten twistor-string for N=4 super-Yang-Mills coupled to N=4 conformal supergravity, and the Skinner twistor-string for N=8 supergravity. By considering these string-like theories, we can study factorization at the level of the worldsheet before any Wick contractions or integrals have been performed; this is much simpler than considering the factorization properties of the amplitudes themselves. In Skinner's twistor-string this entails the addition of worldsheet gravity as well as a formalism that represents all external states in a manifestly symmetric way, which we develop explicitly at genus zero. We confirm that the scattering amplitudes of Skinner's theory, as well as the gauge theory amplitudes for the planar sector of the Berkovits-Witten theory, factorize appropriately at genus zero. In the non-planar sector, we find behavior indicative of conformal gravity in the Berkovits-Witten twistor-string. We contrast factorization in twistor-strings with the story in ordinary string theory, and also make some remarks on higher genus factorization and disconnected prescriptions.
Highlights
Factorization at the level of the worldsheet before any Wick contractions or integrals have occurred
Skinner found a worldsheet theory whose genus zero scattering amplitudes correspond to this formula [22], raising the possibility that higher loop supergravity amplitudes could be computed using this novel twistor-string at higher genus
Given the RSV or Cachazo-Skinner formula, one might ask: what is the utility of having a worldsheet theory which produces the formula at genus zero? In this paper, we provide one answer to this question: multiparticle factorization for these formulae is obtained organically using the worldsheet theory
Summary
We introduce the two worldsheet theories we will study for the remainder of this paper. In Skinner’s twistor-string it is most natural to calculate scattering amplitudes in a formalism where some vertex operators are fixed and the remainder are integrated [22] This is due to the fermionic structure of the worldsheet, which is a (1|2)-dimensional split supermanifold. We need to put all external states on the same footing at the level of the worldsheet correlator — before any Wick contractions or integrals have been performed This entails using fixed vertex operators for all external states, at the cost of introducing Picture Changing Operators (PCOs) which ensure that we still obtain a top-degree form on the fermionic moduli space. With Q the relevant BRST operator and Θ the Heavyside step function Constructing these operators for the Skinner theory allows us to set up scattering amplitudes which are manifestly permutation symmetric with respect to external states at the level of the worldsheet. The reader who is already familiar with these theories may wish to skim this section, moving on the the discussion of worldsheet gravity and factorization that follows
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