Abstract
For a perturbation of the state of a conformal field theory (CFT), the response of the entanglement entropy is governed by the so-called “first law” of entanglement entropy, in which the change in entanglement entropy is proportional to the change in energy. Whether such a first law holds for other types of perturbations, such as a change to the CFT Lagrangian, remains an open question. We use holography to study the evolution in time of entanglement entropy for a CFT driven by a -linear source for a conserved current or marginal scalar operator. We find that although the usual first law of entanglement entropy may be violated, a first law for the rates of change of entanglement entropy and energy still holds. More generally, we prove that this first law for rates holds in holography for any asymptotically ()-dimensional anti–de Sitter metric perturbation whose dependence first appears at order in the Fefferman-Graham expansion about the boundary at .
- Received 6 July 2017
DOI:https://doi.org/10.1103/PhysRevD.96.066028
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