Entanglement of local operators in large-N conformal field theories

Abstract

In this paper, we study Renyi and von Neumann entanglement entropy of excited states created by local operators in large-|$N$| (or large-central-charge) conformal field theories (CFTs). First we point out that a naive large-|$N$| expansion can break down for the von Neumann entanglement entropy, while it does not for the Renyi entanglement entropy. This happens even for the excited states in free Yang–Mills theories. Next, we analyze strongly coupled large-|$N$| CFTs from both the field-theoretic and holographic viewpoints. We find that the Renyi entanglement entropy of the excited state, produced by a local operator, grows logarithmically under its time evolution and its coefficient is proportional to the conformal dimension of the local operator.