Title: Relative Entropy in CFT,
Abstract: By using Araki's relative entropy, Lieb's convexity and the theory of
singular integrals, we compute the mutual information associated with free
fermions, and we deduce many results about entropies for chiral CFT's which are
embedded into free fermions, and their extensions. Such relative entropies in
CFT are here computed explicitly for the first time in a mathematical rigorous
way. Our results agree with previous computations by physicists based on
heuristic arguments; in addition we uncover a surprising connection with the
theory of subfactors, in particular by showing that a certain duality, which is
argued to be true on physical grounds, is in fact violated if the global
dimension of the conformal net is greater than $1.$