2021/12/27 by Chethan Krishnan, Krishnan, Chethan, Vyshnav Mohan +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.2112.13783
Lots of pictures
arxiv created 2021/12/27 · openalex publication_date 2021/12/27 · arxiv updated 2021/12/28 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28
Areas of extremal surfaces anchored to sub-regions on screens in Minkowski space satisfy various entanglement entropy inequalities. In 2+1 dimensions where the arguments are simplest, we demonstrate (a) monogamy of mutual information, (b) various versions of (strong) subadditivity, (c) various inequalities involving the entanglement of purification, as well as (e) reflection inequality and (f) Araki-Lieb inequality. Just as in AdS, Linden-Winter and the tower of Cadney-Linden-Winter inequalities are satisfied trivially. All of these are purely geometric (and therefore unambiguous) statements, and we expect them to hold semi-classically when GN → 0. The results of arXiv:2103.17253 suggest that it is unlikely that there is non-analyticity at GN=0. These observations have relevance for the Page phase transition in flat space black holes observed with respect to a screen in arXiv:2005.02993 and arXiv:2006.06872. In particular, they constitute a Lorentzian argument that these extremal surface transitions are indeed phase transitions of some suitably defined entanglement entropy associated to subregions on the screen.