Lower bound on the entropy of boundaries and junctions in 1+1d quantum   critical systems
  A lower bound is derived for the boundary entropy s = ln g of a 1+1d quantum critical system with boundary, under the conditions that the bulk conformal central charge c is >=1 and the most relevant bulk scaling dimension is >(c-1)/12. This is the first general restriction on the possible values of g for bulk critical systems with c >= 1. 
Daniel Friedan, Anatoly Konechny, and Cornelius Schmidt-Colinet
hep-th cond-mat.stat-mech quant-ph