Abstract
Recently two of the authors presented a spinorial extension of the scattering equations, the polarized scattering equations that incorporates spinor polarization data. These led to new worldsheet amplitude formulae for a variety of gauge, gravity and brane theories in six dimensions that naturally incorporate fermions and directly extend to maximal supersymmetry. This paper provides a number of improvements to the original formulae, together with extended details of the construction, examples and full proofs of some of the formulae by BCFW recursion and factorization. We show how our formulae reduce to corresponding formulae for maximally supersymmetric gauge, gravity and brane theories in five and four dimensions. In four dimensions our framework naturally gives the twistorial version of the 4d ambitwistor string, giving new insights into the nature of the refined and polarized scattering equations they give rise to, and on the relations between its measure and the CHY measure. Our formulae exhibit a natural double-copy structure being built from ‘half-integrands’. We give further discussion of the matrix of theories and formulae to which our half-integrands give rise, including controversial formulae for amplitudes involving Gerbes.
Highlights
Worldsheet approaches to scattering amplitudes generate perhaps the most compact and mathematically structured formulae for tree-level S-matrices and loop integrands available
This paper provides a number of improvements to the original formulae, together with extended details of the construction, examples and full proofs of some of the formulae by BCFW recursion and factorization
In this article we have argued that the polarized scattering equations provide a natural generalization of the twistor and ambitwistor supersymmetric formulae from four dimensions
Summary
Worldsheet approaches to scattering amplitudes generate perhaps the most compact and mathematically structured formulae for tree-level S-matrices and loop integrands available. The last two named authors of this paper introduced a distinct approach [17] based on extending the scattering equations to incorporate polarization data These polarized scattering equations have a geometric origin in string theories in sixdimensional ambitwistor space expressed in twistorial coordinates ( complete worldsheet theories that give rise to the full supersymmetric worldsheet formulae remain lacking). They were used to obtain compact formulae for amplitudes for a full range of six-dimensional theories, without any awkward distinction between even and odd numbers of particles for gauge and gravity theories. There is some discussion of ambitwistor worldsheet models and the controversial formulae for Gerbe theories with (2, 0), (3, 1) and (4, 0) supersymmetry
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