Modular hamiltonians in 2d CFT

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I enumerate the cases in 2d CFT when the modular hamiltonian (log of the reduced density matrix) may be written as an appropriate integral over the energy-momentum tensor times a local weight. This includes known examples as well as new time-dependent ones. In all these cases the entanglement spectrum is that of an appropriate boundary CFT. I point out the obstruction to the existence of such a result for more complicated bipartitions of the space. This is joint work with Erik Tonni

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