Twistor Space and Celestial Holography

Abstract

This thesis is divided into 4 main parts. The first part is review material, consisting of short descriptions of prerequisite background material, as well as references to good sources that cover the material in more depth. The second part is a discussion of twistor methods for H$^3_\mathbb{C}$ and H$^5_\mathbb{C}$, the complexification of 3 and 5 dimensional hyperbolic space. We discuss the minitwistor space of the bulk and its relation to the ambitwistor space of the boundary. The third part of my thesis is a paper on spectral flow and localisation in AdS$_3$ string theory. The fourth and final part of my thesis is a discussion of off-shell Celestial holography. There is a short appendix consisting of several calculations, intended as supplementary material for the main text.