Abstract
Recent progress on scattering amplitudes in super Yang--Mills and superstring theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang--Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. In this work we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between color and kinematics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.
Highlights
In recent years, the super-Poincare covariant description [1] of ten-dimensional super YangMills theory (SYM) has been extensively used to compute scattering amplitudes in string and field theory
The appearance of the linearized versions Aα(x, θ), Am(x, θ), W α(x, θ) and F mn(x, θ) of (1.1) in the massless vertex operators of the pure spinor superstring [2] have brought these superfields to the forefront of perturbation theory: they compactly encode the kinematic factors of scattering amplitudes in string and field theory
This for instance applies to the general box and double-box diagram displayed in figure 2 where the multiparticle labels A, B, C and D refer to appropriate superfields with the symmetry (1.7)
Summary
The super-Poincare covariant description [1] of ten-dimensional super YangMills theory (SYM) has been extensively used to compute scattering amplitudes in string and field theory. The appearance of the linearized versions Aα(x, θ), Am(x, θ), W α(x, θ) and F mn(x, θ) of (1.1) in the massless vertex operators of the pure spinor superstring [2] have brought these superfields to the forefront of perturbation theory: they compactly encode the kinematic factors of scattering amplitudes in string and field theory. As described in [3, 4, 6], the precise definition of KP used an intuitive mapping between planar binary trees (or cubic graphs) and Lie symmetry-satisfying multiparticle superfields, dressed with the propagators of the graph. These Berends-Giele currents elegantly capture kinematic factors of multiparticle amplitudes in both string and field-theory. As one of the main result of this article, we provide an alternative definition of BerendsGiele currents which tremendously simplifies the construction of earlier work [6] while preserving their equations of motion
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