Precise lower bound on Monster brane boundary entropy

In this paper we develop further the linear functional method of deriving lower bounds on the boundary entropy of conformal boundary conditions in 1+1 dimensional conformal field theories (CFTs). We show here how to use detailed knowledge of the bulk CFT spectrum. Applying the method to the Monster CFT with c=\bar c=24 we derive a lower bound s > - 3.02 x 10^{-19} on the boundary entropy s=ln g, and find compelling evidence that the optimal bound is s>= 0. We show that all g=1 branes must have the same low-lying boundary spectrum, which matches the spectrum of the known g=1 branes, suggesting that the known examples comprise all possible g=1 branes, and also suggesting that the bound s>= 0 holds not just for critical boundary conditions but for all boundary conditions in the Monster CFT. The same analysis applied to a second bulk CFT -- a certain c=2 Gaussian model -- yields a less strict bound, suggesting that the precise linear functional bound on s for the Monster CFT is exceptional.