规范不变性与阿德勒零点的唯一性
Uniqueness from gauge invariance and the Adler zero
摘要：
在本文中，我们提供了一些arXiv：1612.02797中提出的唯一性结果的详细证明。我们证明：（1）Yang-Mills和广义相对论树能级振幅完全由$n-1$粒子的规范不变性决定，对奇异性结构作了最小的假设;（2）标量非线性西格玛模型和Dirac-Born-Infeld树能级振幅通过对$n-1$粒子施加全定域性和Adler零条件（消失在单软极限中）来固定.我们证明了杨米尔斯和广义相对论的单软展开式和NLSM和DBI的双软展开式的唯一性。我们进一步提出了一个更大的猜想杨-米尔斯振幅的证据，即最大约束规范不变性单独导致本地性和幺正性，没有任何假设的奇点的存在。在这种情况下，解不是唯一的，而是振幅分子的线性组合。
英文摘要：
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.
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