An Emergent Area Operator in 2d CFT

          @misc{ pirsa_PIRSA:25060006,
            doi = {10.48660/25060006},
            url = {https://pirsa.org/25060006},
            author = {Soni, Ronak},
            keywords = {Quantum Gravity, Quantum Information},
            language = {en},
            title = {An Emergent Area Operator in 2d CFT},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {jun},
            note = {PIRSA:25060006 see, \url{https://pirsa.org}}
          }
          

Abstract

The Ryu-Takayanagi formula implies that the entropy, a non-linear function of the state, is an observable in the semiclassical limit. This is a general phenomenon in a class of quantum error-correcting codes (QECC), but few specific area operators in the boundary CFT. In this work, I define a specific code in a holographic 2d CFT that includes all thermofield double states with arbitrary amounts of time evolution, but no bulk local degrees of freedom. While the naive area operator vanishes, it is possible to write down an area operator for appropriately classical states; the answer matches with previous results obtained from bulk considerations. Interestingly, this area operator involves an explicit coarse-graining. This suggests a construction for a non-isometric holographic map for these states.