Untitled Peer review Boundary Liouville Field TheoryI. Boundary State and Boundary Two-point Function Alexander ZamolodchikovItem

The manuscript presents a detailed construction of boundary Liouville field theory based onconformal bootstrap, analytic continuation, and duality arguments. The results are technicallysophisticated and of potential interest.However, several steps that are essential for establishing the mathematical completeness ofthe construction are currently implicit. Clarifying these points would be important in orderto assess whether the framework defines a fully consistent quantum field theory, rather than aformally constrained set of correlation functions.Below I list a number of technical questions whose resolution appears necessary.