Lower bound on the entropy of boundaries and junctions in (1+1)-dimensional quantum critical systems

A lower bound is derived for the boundary entropy s= lng of a (1+ 1)-dimensional quantum
critical system with boundary under the conditions c grater or equal to 1 on the bulk conformal central charge and Delta_1 grater or equal than (c-1)/12 on the most relevant bulk scaling dimension. This is the first general restriction on the possible values of g for bulk critical systems with c grater or equal than 1.