Modular Hamiltonians of excited states, OPE blocks and emergent bulk fields

Understand

We study the entanglement entropy and the modular Hamiltonian of slightly excited states reduced to a ball shaped region in generic conformal field theories.

• We set up a formal expansion in the one point functions of the state in which all orders are explicitly given in terms of integrals of multi-point functions along the vacuum modular flow, without a need for replica index analytic continuation.
• We show that the quadratic order contributions in this expansion can be calculated in a way expected from holography, namely via the bulk canonical energy for the entanglement entropy, and its variation for the modular Hamiltonian.
• The bulk fields contributing to the canonical energy are defined via the HKLL procedure.