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Holographic Conformal Blocks


The conformal block decomposition of field theory correlation functions is a powerful way of disentangling dynamical from universal properties of a field theory. The work on this thesis focuses on the holographic description of conformal blocks in the framework of the AdS/CFT correspondence.

We begin by stablishing the correspondence between global conformal blocks in any number of space-time dimensions and ``geodesic Witten diagrams'' which are essentially ordinary Witten diagrams, except that vertices are not integrated over all of AdS, but only over bulk geodesics connecting boundary operators.

We then turn to the study of Virasoro blocks in two dimensions. These are much richer objects that are known only in certain limits for the central charge and the conformal dimensions of the operators in question. We provide a holographic description that correctly reproduces all known Virasoro blocks.

We finish with the bulk description of blocks involving more complicated CFT symmetries. The holographic picture involves Wilson lines merging at a bulk vertex.

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