Ambitwistor strings and the complex geometry of the S-matrix

野心空间是复杂时空中具有复杂类光测地线的空间。它们最初是由Witten和Isenberg， Yasskin & Green在1978年引入的，用于将Ward的自双规范场的扭扭结构扩展到一般规范场。这些想法也直接延伸到重力。它们将规范或引力场的信息编码到测量空间复杂结构的变形中。因此，他们将这些出了名的困难的偏微分方程的分析转化为复杂的分析。上个世纪提供的场方程的公式很难使用，直到去年，这个框架几乎没有什么主要应用。然而，PI和合作者的工作已经表明，对于规范场和引力场的散射，在空域空间中的全纯弦理论产生的微扰公式比迄今为止认为的要简单得多，特别是为Cachazo， He和Yuan的非凡公式提供了基础理论，也产生了其他新的非常简单的公式。这些公式的简单性是一个确凿的证据，证明了规范和重力理论的完全非线性的雄心公式的存在，尽管这些理论缺乏完全的可积性，但它也反映了这种非凡的简单性。弦的使用允许将复杂的多维复杂分析简化为更易于处理的黎曼曲面的复杂分析。这项研究计划的最终目的是获得这样一个完全非线性的结构，可以为理解这些方程的数学和物理提供一个重要的新工具，无论是经典的还是量子力学的。然而，有许多机会性的项目正在进行中，这些项目将在新的背景下（包括经典和量子）产生显著的振幅新公式，并产生关于规范和重力s矩阵的一般结构的新定理。

Ambitwistor spaces are spaces of complex light-like geodesics in complexified space-times. They were originally introduced by Witten and by Isenberg, Yasskin & Green in 1978 to extend Ward's twistor constructions for self-dual gauge fields to general gauge fields. The ideas extend directly also to gravity. They encode the information of a gauge or gravitational field into the deformation of the complex structure of the ambitwistor space. They therefore convert the analysis of these notoriously difficult partial differential equations into complex analysis. The formulation of the field equations provided in the last century was sufficiently difficult to use that, until last year, the framework had few major applications. However, work of the PI and collaborators has shown that holomorphic string theories in ambitwistor space yield dramatically simpler perturbative formulae for the scattering of gauge and gravitational fields than had hitherto been thought to exist and in particular give the fundamental theory underlying the remarkable formulae of Cachazo, He and Yuan, generating other new remarkably simple formulae also. The simplicity of these formulae is a smoking gun for the existence of a fully nonlinear ambitwistor formulation of gauge and gravity theories that will also reflect this remarkable simplicity despite the lack of complete integrability of these theories. The use of strings allows the reduction of complicated multidimensional complex analysis to the much more tractable complex analysis of Riemann surfaces. The ultimate purpose of this research proposal is to obtain such a fully nonlinear construction that can provide a major new tool for understanding the mathematics and physics of these equations, both classically and quantum mechanically. However, there are many opportunistic projects en route that will generate remarkable new formulae for amplitudes in new contexts, both classical and quantum, and generate new theorems concerning the general structure of the gauge and gravity S-matrices based on complex analysis in ambitwistor space.