Higher codimension singularities constructing Yang-Mills tree amplitudes. (English) Zbl 1342.81612
Summary: 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.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 32A27 | Residues for several complex variables |
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