Minimax surfaces and the covariant holographic entropy cone

          @misc{ scivideos_PIRSA:22060056,
            doi = {10.48660/22060056},
            url = {https://pirsa.org/22060056},
            author = {Grimaldi, Guglielmo},
            keywords = {Other Physics},
            language = {en},
            title = {Minimax surfaces and the covariant holographic entropy cone},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060056 see, \url{https://scivideos.org/pirsa/22060056}}
          }
          

Abstract

I will discuss work-in-progress for defining a new proposal for the covariant holographic entanglement entropy. The proposal instructs us to find maximal spacelike codimension-2 surfaces on timelike hypersurfaces in the bulk, followed by a minimization among all possible hypersurfaces in the right homology class. We describe and prove various properties of such minimax surfaces, and argue for their equivalence with the more familiar HRT and maximin proposals. Finally, we give compelling reasons to be interested in yet another entanglement entropy proposal: minimax surfaces allow us to prove all higher entropy cone inequalities, showing that the RT and HRT holographic entropy cones are indeed equivalent.