Entanglement of Local Operators in large N CFTs

TL;DR

The paper investigates how local operator excitations affect entanglement in large-N CFTs, uncovering a fundamental difference between Renyi and von Neumann entropies under large-N scaling. Using a blend of replica-field theory calculations in free and 2d CFTs, plus holographic analyses with topological AdS black holes and geodesic approximations, it shows that Renyi entropies exhibit logarithmic time growth with coefficients tied to operator dimensions, while von Neumann entropy in the same setting can be nonperturbatively enhanced and requires backreaction to resolve. Across dimensions, the results connect field-theoretic expectations to holographic duals, revealing a consistent picture in which Renyi entropies grow and saturate, whereas von Neumann entropy demands nonperturbative corrections and careful treatment of the large-N limit. The work thus deepens our understanding of entanglement dynamics after local quenches in holographic and large-N CFTs, and highlights distinct regimes where field theory and gravity computations agree or necessitate nonperturbative physics.

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.

Figures (4)

• Figure 1: The $n$-sheeted geometry $\Sigma_n$, constructed by gluing the subsystem A on a sheet to another subsystem A on other sheet.
• Figure 2: The plots of $\Delta S^{(2)}_A$ (green) and $\Delta S^{(3)}_A$ (blue) as functions of the time $t$ in the $\epsilon \rightarrow 0$ limit (we chose $l=10$). The red horizontal corresponds to the late time value $\log{2}$.
• Figure 3: The two dominant diagrams for the $4$th Renyi entanglement entropy $\Delta S^{(4)}_A$ in the large $N$ and $\epsilon \rightarrow 0$ limit.
• Figure 4: This is the plot of $\Delta S^{(2)}_A$ (blue) as function of $t$ in the $\epsilon \rightarrow 0$ limit. Here we chose $l=10$, $n=2$ and $J=3$. The red line corresponds to the late time value $5\log{2}$.