arXiv 0801.23852008-01-16hep-th

关于规范理论和引力中的树振幅

On Tree Amplitudes in Gauge Theory and Gravity

Nima Arkani-Hamed, Jared Kaplan

备注：: 22 pages, 3 figures
发表信息：: JHEP 0804:076,2008
DOI：: 10.1088/1126-6708/2008/04/076

摘要：

BCFW递归关系提供了一种计算规范理论和引力中树振幅的强有力的方法，但只有当两个动量在一个特定的复方向上无穷大时，某些振幅消失时才成立。这是一个非常令人惊讶的性质，因为每个费曼图都在无穷大的动量下发散。在本文中，我们给出了一个简单的物理理解的振幅在这个极限，这对应于一个硬粒子与（复杂）轻动量运动在软背景中，可以方便地使用背景场方法利用背景光锥规范进行研究。一个重要的作用是增强自旋对称性在无限动量-一个单一的副本的“洛伦兹”群的规范理论和两个副本的引力-这与沃德恒等式一起给出了一个系统的扩展振幅在大动量。我们用它来研究各种理论中的树振幅，特别是证明某些纯规范和重力振幅在无穷远处消失。因此，BCFW递推关系可以用来计算任意维数下的完全一般的胶子和引力子树振幅。我们简要地评论这些结果的影响，计算大规模的4D振幅的KK减少，以及理解意外的取消，最近被发现在环路级重力振幅。

英文摘要：

The BCFW recursion relations provide a powerful way to compute tree amplitudes in gauge theories and gravity, but only hold if some amplitudes vanish when two of the momenta are taken to infinity in a particular complex direction. This is a very surprising property, since individual Feynman diagrams all diverge at infinite momentum. In this paper we give a simple physical understanding of amplitudes in this limit, which corresponds to a hard particle with (complex) light-like momentum moving in a soft background, and can be conveniently studied using the background field method exploiting background light-cone gauge. An important role is played by enhanced spin symmetries at infinite momentum--a single copy of a "Lorentz" group for gauge theory and two copies for gravity--which together with Ward identities give a systematic expansion for amplitudes at large momentum. We use this to study tree amplitudes in a wide variety of theories, and in particular demonstrate that certain pure gauge and gravity amplitudes do vanish at infinity. Thus the BCFW recursion relations can be used to compute completely general gluon and graviton tree amplitudes in any number of dimensions. We briefly comment on the implications of these results for computing massive 4D amplitudes by KK reduction, as well understanding the unexpected cancelations that have recently been found in loop-level gravity amplitudes.

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