Precise lower bound on Monster brane boundary entropy

TL;DR

This paper refines the linear functional method to derive a near-zero lower bound on boundary entropy in the Monster CFT, providing evidence that the minimal boundary entropy is zero and that known g=1 branes are all possible low-lying boundary states.

Contribution

It introduces a detailed method leveraging bulk spectrum knowledge to establish tight lower bounds on boundary entropy in 1+1D CFTs, especially for the Monster CFT.

Findings

Derived a lower bound s > -3.02 x 10^{-19} for the Monster CFT boundary entropy.

Provided evidence that the minimal boundary entropy s >= 0 for the Monster CFT.

Suggested that all g=1 branes share the same low-lying spectrum, matching known examples.

Abstract

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.