Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions

TL;DR

The paper develops a ten-dimensional spinor-helicity formalism for massless states in N=1 SYM and uses it to establish a dual conformal symmetry of tree-level amplitudes. It introduces a ten-dimensional dual conformal generator C^μ, compatible with supersymmetry and preserved by a ten-dimensional BCFW recursion that includes both bosonic and fermionic deformations. Through dimensional reduction, the results connect to the well-known four-dimensional dual conformal structure and offer insights into loop integrands in lower dimensions. The work also clarifies the role of region momenta x_i and provides a framework for exploring higher-dimensional amplitudes and potential dual descriptions.

Abstract

The spinor helicity formalism in four dimensions has become a very useful tool both for understanding the structure of amplitudes and also for practical numerical computation of amplitudes. Recently, there has been some discussion of an extension of this formalism to higher dimensions. We describe a particular implementation of the spinor-helicity method in ten dimensions. Using this tool, we study the tree-level S-matrix of ten dimensional super Yang-Mills theory, and prove that the theory enjoys a dual conformal symmetry. Implications for four-dimensional computations are discussed.

Figures (1)

• Figure 1: The structure of the $k$th BCFW diagram contributing to an $n$ point function.