Twistors and Duality at the String Scale

在过去的几十年里，对偶对称在发展我们对弦理论的理解方面发挥了显著的作用。也许最引人注目的是ADS/CFT对应，它假定无引力的共形规范理论和渐近ADS空间中的弦理论在量子水平上是等价的。尽管有许多这种对应的例子，但实现这种等价性的详细机制仍然是个谜，这主要是因为当弦张力与理论中的其他标度相比很小时，对弦理论的理解不完整。最近，在ADS_3背景下对弦理论的理解取得了进展，其中弦的扩展性质变得重要。这些模型与Twistor理论有着惊人但仍然神秘的关系。这个项目将在小张力极限下研究Twistor弦结构和弦理论之间的这种意想不到的关系。尤其令人感兴趣的是，当弦效应变得重要，传统的超引力几何直觉不再适用时，Twistor理论在描述时空的数学结构方面所扮演的角色。

Duality symmetries have played a striking role in developing our understanding of String Theory over the past few decades. Perhaps the most striking has been the AdS/CFT correspondence which posits an equivalence at the quantum level between conformal gauge theories without gravity, and String theories in asymptotically AdS space. Though there are many examples of this correspondence, the detailed mechanism by which this equivalence is realised is still mysterious, largely due to an incomplete understanding of the String Theory when the string tension is small compared to other scales in the theory. Recently, progress has been made in understanding string theory in AdS_3 backgrounds where the extended nature of the string becomes important. These models have a striking, yet still mysterious, relationship to Twistor theory. This project will investigate this unexpected relationship between Twistor string constructions and string theory in the small tension limit. Of particular interest will be understanding the role Twistor theory plays in describing the mathematical structure of spacetime when stringy effects become important and conventional geometric intuition from supergravity is no longer adequate.