Conformal blocks are building blocks of correlation functions in conformal field theories (CFTs). They neatly encode the universal information dictated by conformal symmetry and separate it from the dynamical information which depends on the particular theory. Conformal blocks merit an in-depth study as is evidenced by their extensive applications in the study of bulk locality in the AdS/CFT correspondence and the recent conformal bootstrap program. The vacuum Virasoro blocks in the semi-classical (large central charge) limit is known to compute the leading order contribution to the Rényi entropy. Moreover, the semi-classical Virasoro blocks along with conformal bootstrap feature in a proof of the cluster decomposition principle for AdS3/CFT2.
In this thesis, conformal field theory and its necessary ingredients are briefly reviewed. Conformal blocks from the exchange of a spinless operator are evaluated by holographic computations of geodesic Witten diagrams for AdSd+1/CFTd. The results are verified against the Casimir operator method of Dolan and Osborn. Virasoro blocks in various semi-classical limits are discussed, and holographic Virasoro blocks are calculated in the global, heavy-light, and perturbative heavy, and the results are verified using the monodromy method.
Finally, defect conformal field theories (dCFTs) are introduced and, as an original contribution, an integral expression for defect conformal blocks is obtained, which is expected to precisely match the corresponding result in dCFT literature.
