ANNULÉ ET REPORTÉ
In this talk we will revisit the bootstrap hypothesis in the two-dimensional case from a mathematical perspective. The bootstrap equations is a consistency for the CFT four-point correlation functions. Therefore, the following question is not mathematically clear: (Math Question) If the four-point correlation functions satisfy the bootstrap equations, can we define a multi-point correlation functions? (Is it convergent and consistent?) After introducing the notion of a full vertex algebra, which is equivalent to the fact that the four-point correlation functions satisfy the bootstrap equations, we will explain that all n-point correlation functions converge and are consistent when the full vertex algebra satisfies certain finiteness. An crucial step in the proof is to show that the operad of configuration spaces acts on representations of the full vertex algebra (under the finiteness assumption). We will explain this idea in detail.
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Slava Rychkov & Ryan Thorngren
