Simple superamplitudes in higher dimensions

TL;DR

The paper extends spinor-helicity and on-shell superspace techniques to general even dimensions, constructing a fermionic delta function that solves on-shell SUSY Ward identities and enabling compact three-, four-, and five-point superamplitudes in $D=8$ Yang–Mills and $D=10$ IIB supergravity. It introduces a dimension-spanning on-shell recursion (SUSY BCFW) and demonstrates explicit three- and four-point amplitudes, including their string-theoretic extensions via Gamma functions and KLT relations, with dimensional reductions reproducing known 4D results. A key result is the uniform treatment of higher-dimensional amplitudes through a unified spinor-helicity formalism, the preservation of supermomentum in shifts, and the explicit five-point recursion example, illustrating the practical utility of the method. The framework provides a compact, manifestly SUSY toolkit for higher-dimensional amplitudes, with potential applications to loop calculations, string theory amplitudes, and cross-dimensional consistency checks.

Abstract

We provide simple superspaces based on a formulation of spinor helicity in general even dimensions. As a distinguishing feature these spaces admit a fermionic super-momentum conserving delta function solution to the on-shell supersymmetry Ward identities. Using these solutions, we present beautifully simple formulae for the complete three, four and five point superamplitudes in maximal super Yang-Mills theory in eight dimensions, and for the three and four point superamplitudes in ten dimensional type IIB supergravity. In addition, we discuss the exceptional kinematics of the three point amplitude, and the supersymmetric spinorial BCFW recursion, in general dimensions.