We analyze how excitations affect the entanglement entropy for an arbitrary entangling interval in a 2d conformal field theory (CFT) using the holographic entanglement entropy techniques as well as direct CFT computations. We introduce the excitation entanglement entropy ${\mathrm{\Delta }}_{h}S$, the difference between the entanglement entropy generic excitations and their arbitrary conformal descendants denoted through $h$. The excitation entanglement entropy, unlike the entanglement entropy, is a finite quantity (independent of the cutoff), and hence a good physical observable. We show that the excitation entanglement entropy for any given interval is uniquely specified by a local second order differential equation sourced by the one point function of the energy momentum tensor computed in the excited background state, and two boundary and smoothness conditions. We analyze low and high temperature behavior of the excitation entanglement entropy and show that ${\mathrm{\Delta }}_{h}S$ grows as a function of temperature. We prove an “integrated positivity” for the excitation entanglement entropy, that although ${\mathrm{\Delta }}_{h}S$ can be positive or negative, its average value is always positive. We also discuss the mutual and multipartite information and (strong) subadditivity inequality in the presence of generic excitations and their conformal descendants.

• Received 10 May 2016

DOI:https://doi.org/10.1103/PhysRevD.94.126006