Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes

Abstract

Yang-Mills tree-level amplitudes contain singularities of codimension one like collinear and multi-particle factorizations, codimension two such as soft limits, as well as higher codimension singularities. Traditionally, BCFW-like deformations with one complex variable were used to explore collinear and multi-particle channels. Higher codimension singularities need more complex variables to be reached. In this paper, along with a discussion on higher singularities and the role of the global residue theorem in this analysis, we specifically consider soft singularities. This is done by extending Risager's deformation to a ${\mathbb{C}}^2$-plane, i.e., two complex variables. The two-complex-dimensional deformation is then used to recursively construct Yang-Mills tree amplitudes.

17 pages, 5 figures

References in corpus (6)

• Tree Level Recursion Relations In General Relativity
• The Yangian origin of the Grassmannian integral
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• MHV Diagrams in Momentum Twistor Space
• From Twistor String Theory To Recursion Relations
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity