2016/12/31 by Laurentiu Rodina
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep09(2019)084
published as JHEP09(2019)084 · 26 pages; v2: typos corrected, added references; v3: minor revision
arxiv created 2019/08/05 · arxiv updated 2019/09/17
In this paper we provide detailed proofs for some of the uniqueness results presented in arXiv:1612.02797. We show that: (1) Yang-Mills and General Relativity tree-level amplitudes are completely determined by gauge invariance in n-1 particles, with minimal assumptions on the singularity structure, (2) scalar non-linear sigma model and Dirac-Born-Infeld tree-level amplitudes are fixed by imposing full locality and the Adler zero condition (vanishing in the single soft limit) on n-1 particles. We complete the proofs by showing uniqueness order by order in the single soft expansion for Yang-Mills and General Relativity, and the double soft expansion for NLSM and DBI. We further present evidence for a greater conjecture regarding Yang-Mills amplitudes, that a maximally constrained gauge invariance alone leads to both locality and unitarity, without any assumptions on the existence of singularities. In this case the solution is not unique, but a linear combination of amplitude numerators.