Twistors and Duality at the String Scale

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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.