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Twistor Space and Celestial Holography https://doi.org/10.17863/CAM.112793 Seet, Sean Skinner, David 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. University of Cambridge 2024-06-14 Thesis Doctoral Doctor of Philosophy (PhD) eng Supported by the Trinity College Internal Graduate Studentship. Partially supported by STFC HEP Theory Consolidated grant ST/T000694/1. Partially supported by the Simons Collaboration on Celestial Holography. https://www.repository.cam.ac.uk/handle/1810/374919 https://www.repository.cam.ac.uk/bitstreams/5318fd73-7006-4563-8cb3-c7c63bfe175f/download cc37e1f2b14267333d9e47aea4fc672d https://www.repository.cam.ac.uk/bitstreams/a63e7194-1cec-474b-9ae7-f9ffdc4e3047/download 87eda9de84448d1f82354d60eee3eb5f https://www.rioxx.net/licenses/all-rights-reserved/ Celestial Holography High Energy Physics Quantum Field Theory Theoretical Physics Twistor