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The holographic relation between local boundary conformal quantum fieldtheories (BCFT) and their non-local boundary restrictions is reviewed, andnon-vacuum BCFT's, whose existence was conjectured previously, are constructed.Comment: 16 pages. Contribution to "Rigorous Quantum Field Theory", Symposium  in honour of J. Bros, Paris, July 2004. Based on joint work math-ph/0405067  with R. Long

On Local Boundary CFT and Non-Local CFT on the Boundary