Entanglement of Local Operators in large N CFTs

TL;DR

This paper investigates how local operators affect entanglement entropy in large N conformal field theories, revealing differences in behavior between Renyi and von-Neumann entropies and showing logarithmic growth linked to operator dimensions.

Contribution

It uncovers the breakdown of large N expansion for von-Neumann entropy and analyzes entanglement dynamics in both free and strongly coupled large N CFTs using field theory and holography.

Findings

Large N expansion fails for von-Neumann entropy but not for Renyi entropy.

Renyi entanglement entropy grows logarithmically over time.

Growth coefficient is proportional to the local operator's conformal dimension.

Abstract

We study Renyi and von-Neumann entanglement entropy of excited states created by local operators in large N (or large central charge) CFTs. First we point 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 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.