Is the EMI model a QFT? An inquiry on the space of allowed entropy functions

• Published in: The journal of high energy physics Vol. 2021; no. 8; pp. 1 - 47
• Main Authors: Agón, César A., Bueno, Pablo, Casini, Horacio
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 17.08.2021; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Clustering; Conformal Field Theory; Elementary Particles; Entropy; Fermions; Field Theories in Higher Dimensions; High energy physics; Operators (mathematics); Physical properties; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry; Conformal Field Theory; Field Theories in Higher Dimensions
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2021)084

A bstract The mutual information I ( A, B ) of pairs of spatially separated regions satisfies, for any d -dimensional CFT, a set of structural physical properties such as positivity, monotonicity, clustering, or Poincaré invariance, among others. If one imposes the extra requirement that I ( A, B ) is extensive as a function of its arguments (so that the tripartite information vanishes for any set of regions, I 3 ( A, B, C ) ≡ 0), a closed geometric formula involving integrals over ∂A and ∂B can be obtained. We explore whether this “Extensive Mutual Information” model (EMI), which in fact describes a free fermion in d = 2, may similarly correspond to an actual CFT in general dimensions. Using the long-distance behavior of I EMI ( A, B ) we show that, if it did, it would necessarily include a free fermion, but also that additional operators would have to be present in the model. Remarkably, we find that I EMI ( A, B ) for two arbitrarily boosted spheres in general d exactly matches the result for the free fermion current conformal block G ∆ = d − 1 , J = 1 d . On the other hand, a detailed analysis of the subleading contribution in the long-distance regime rules out the possibility that the EMI formula represents the mutual information of any actual CFT or even any limit of CFTs. These results make manifest the incompleteness of the set of known constraints required to describe the space of allowed entropy functions in QFT.