Gravity in Twistor Space and its Grassmannian Formulation
Gravity in Twistor Space and its Grassmannian Formulation
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DOI：
10.3842/sigma.2014.051
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发表时间：
2012-07
影响因子：
0.9
通讯作者：
F. Cachazo;L. Mason;David Skinner
中科院分区：
文献类型：
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作者：
F. Cachazo;L. Mason;David Skinner
我们证明了两位作者最近猜想的 N = 8 超引力的完整树级 S 矩阵的公式。证明的继续表明，新公式在相同的初始条件下满足已知物理振幅所满足的相同 BCFW 递归关系。作为证明的一部分，研究了新公式在大 BCFW 变形下的行为。分析的一个意想不到的好处是非常简单地证明了神秘的 1=z 2 引力行为。此外，我们将重力振幅描述为格拉斯曼函数上的多维轮廓积分。格拉斯曼公式的结构非常简单；在 N k 2 MHV 扇区中，被积函数本质上是 MHV 和 MHV 幅度的乘积，分别具有 k + 1 和 n k 1 个粒子。
We prove the formula for the complete tree-level S-matrix of N = 8 super- gravity recently conjectured by two of the authors. The proof proceeds by showing that the new formula satisfies the same BCFW recursion relations that physical amplitudes are known to satisfy, with the same initial conditions. As part of the proof, the behavior of the new formula under large BCFW deformations is studied. An unexpected bonus of the analysis is a very straightforward proof of the enigmatic 1=z 2 behavior of gravity. In addi- tion, we provide a description of gravity amplitudes as a multidimensional contour integral over a Grassmannian. The Grassmannian formulation has a very simple structure; in the N k 2 MHV sector the integrand is essentially the product of that of an MHV and an MHV amplitude, with k + 1 and n k 1 particles respectively.