Liouville theory on the pseudosphere: bulk-boundary structure constant

Liouville field theory on the pseudosphere is considered (Dirichlet conditions). We compute explicitly the bulk-boundary structure constant with two different methods: first we use a suggestion made by Hosomichi [JHEP 0111 (2001) 044] that relates this quantity directly to the bulk-boundary structure constant with Neumann conditions, then we do a direct computation. Agreement is found