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We study the entanglement entropy and the modular Hamiltonian of slightlyexcited states reduced to a ball shaped region in generic conformal fieldtheories. We set up a formal expansion in the one point functions of the statein which all orders are explicitly given in terms of integrals of multi-pointfunctions along the vacuum modular flow, without a need for replica indexanalytic continuation. We show that the quadratic order contributions in thisexpansion can be calculated in a way expected from holography, namely via thebulk canonical energy for the entanglement entropy, and its variation for themodular Hamiltonian. The bulk fields contributing to the canonical energy aredefined via the HKLL procedure. In terms of CFT variables, the contribution ofeach such bulk field to the modular Hamiltonian is given by the OPE blockcorresponding to the dual operator integrated along the vacuum modular flow.These results do not rely on assuming large $N$ or other special properties ofthe CFT and therefore they are purely kinematic.

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