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arXiv 0811.3207hep-th
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利用复分解构造树级Yang-Mills S矩阵

Constructing the Tree-Level Yang-Mills S-Matrix Using Complex Factorization

Philip Schuster, Natalia Toro

备注：
35 pages, 6 figures
发表信息：
JHEP 0906:079,2009
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摘要：

Benincasa和Cachazo在0705.4305中提出了BCFW递归关系和S矩阵上的约束之间的显着联系，他们指出，四粒子振幅的不同BCFW结构的相互一致性产生了非平凡的（但熟悉的）三粒子耦合常数的约束-这些约束包括规范不变性，等效原理，以及自旋>2的非平凡耦合的缺乏。这些约束也可以用较弱的假设导出，通过要求存在四点振幅，这些振幅在所有具有复动量的幺正极限中适当分解。从这个出发点，我们表明，BCFW处方可以被解释为一个算法，完全构建一个树级的S-矩阵，和复杂的因式分解一般BCFW振幅如下从因式分解的四粒子振幅。允许的一组BCFW变形的确定，制定完全作为一个声明的三粒子部门，并只使用复杂的因式分解作为指导。因此，我们基于S矩阵的物理一致性的分析完全独立于场论。我们分析了纯杨米尔斯的情况，并概述了引力的证明。对于杨米尔斯，我们还表明，著名的标度行为的BCFW变形振幅在大z是一个简单的因式分解的后果。对于引力，某些通道中的因式分解需要渐近行为~1/z^2。

英文摘要：

A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates non-trivial (but familiar) constraints on three-particle coupling constants --- these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins >2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior ~1/z^2.

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