Polarized Scattering Equations for 6D Superamplitudes.

Lionel Mason,Yvonne Geyer

doi:10.1103/physrevlett.122.101601

Lionel Mason, Yvonne Geyer

Open Access

https://doi.org/10.1103/physrevlett.122.101601

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Abstract

We introduce a spinorial version of the scattering equations, the polarized scattering equations, that incorporates spinor polarization data. They underpin new formulas for tree-level scattering amplitudes in six dimensions that directly extend to maximal supersymmetry. We find new ingredients for integrands for super Yang-Mills theory, gravity, M5 and D5 branes. We explain how the polarized scattering equations and supersymmetry representations arise from an ambitwistor string with target given by a supertwistor description of 6D superambitwistor space. On reduction to four dimensions, the polarized scattering equations give rise to massive analogues of the 4D refined scattering equations for amplitudes on the Coulomb branch. They give a quite distinct framework from that of Cachazo etal.; in particular, the formulas do not change character from even to odd numbers of particles.

Highlights

Introduction.—Six dimensions has proved to be a fertile arena both for constructing and unifying four-dimensional field theories via dimensional reduction and for studying nontrivial lower dimensional consequences of M theory
Our formulas are motivated by a worldsheet model whose target space is a twistorial representation of 6D
The little group is Spinð4ÞC ≅ SLð2Þþ × SLð2Þ− which can be seen as follows

Summary

Introduction

Introduction.—Six dimensions has proved to be a fertile arena both for constructing and unifying four-dimensional field theories via dimensional reduction and for studying nontrivial lower dimensional consequences of M theory. Generic path integrals in this model localize on polarized scattering equations, formulated in terms of worldsheet spinors incorporating little-group indices and depending on the polarization data of the particles. The Maxwell equations give kABεA 1⁄4 0 1⁄4 kABεB, and the polarization data is encoded in little group spinors εa and εa_

Results

Conclusion