Ambitwistor strings and the complex geometry of the S-matrix

Ambitwistor空间是复杂时空中的复类光测地线空间。它们最初是由维滕和伊森伯格、亚斯金和绿色在1978年引入的，目的是将沃德的扭量构造从自对偶规范场扩展到一般规范场。这些思想也直接延伸到引力。它们将规范场或引力场的信息编码到ambitwistor空间复杂结构的变形中。因此，他们将这些众所周知的困难的偏微分方程的分析转化为复杂的分析。上个世纪提出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重要的应用。然而，PI和合作者的工作表明，在ambitwistor空间中的全纯弦理论对于规范场和引力场的散射给出的微扰公式比迄今为止认为的要简单得多，特别是给出了Cachazo、He和Yuan的著名公式的基本理论，还产生了其他新的非常简单的公式。这些公式的简单性是存在一个完全非线性的ambitwistor制定规范和引力理论，也将反映这种显着的简单性，尽管这些理论缺乏完全可积性的吸烟枪。弦的使用使得复杂的多维复分析可以简化为更容易处理的黎曼曲面的复分析。这项研究提案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学提供一个重要的新工具，包括经典和量子力学。然而，有许多机会主义的项目正在进行中，它们将在新的背景下产生显着的新的振幅公式，包括经典和量子，并产生关于规范和引力S-矩阵的一般结构的新定理，这些定理基于ambitwistor空间中的复分析。

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.