Conformal field theories (CFTs) are important in their application to critical phenomena, as fixed points in the renormalization group of QFTs, and with their role in the AdS-CFT correspondence. The conformal bootstrap has been a useful tool in carving out the space of allowed CFTs and relies on the computation of four point conformal blocks. Currently, a few specific examples for certain spin configurations are worked out in the literature; I set out to obtain general and explicit expressions for these blocks in three and four dimensions, for arbitrary spins. This is accomplished by working in the embedding space formalism of CFTs, deriving projection operators for irreducible representations of the Lorentz group, and enumerating the independent tensor structures that behave as these representations.
Thesis committee: Witold Skiba (advisor), David Poland, Meng Cheng, Keith Baker