TL;DR
This paper rigorously computes relative entropies and mutual information in conformal field theories using advanced mathematical tools, revealing new connections with subfactor theory and clarifying duality properties.
Contribution
It provides the first explicit rigorous computation of relative entropies in CFTs and uncovers a surprising link with subfactor theory and duality violations.
Findings
Explicit formulas for relative entropies in free fermion CFTs
Confirmation of previous heuristic results by physicists
Discovery of duality violation related to global dimension of conformal nets
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
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