Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy

TL;DR

This work investigates entanglement between two interacting CFTs, providing exact and perturbative analyses for massless and massive couplings using Gaussian wave-function and boundary-state replica methods. It reveals a robust volume-law entanglement for massless interactions, with UV-divergent entropy that scales with volume, and shows how massive interactions suppress entanglement, yielding finite or slowly growing behavior. A key contribution is the proposed generalized holographic entanglement entropy, where the internal space (e.g., S^5) is partitioned, yielding a bulk minimal-surface quantity that captures inter-CFT entanglement and scales with N^2, consistent with field-theory results in Coulomb-branch frameworks. The paper also discusses the subtleties of Hilbert-space factorization in AdS/CFT and outlines future directions for connecting these generalized holographic prescriptions to MERA-like pictures and to dynamical, time-dependent CFTs.

Abstract

In this paper we discuss behaviors of entanglement entropy between two interacting CFTs and its holographic interpretation using the AdS/CFT correspondence. We explicitly perform analytical calculations of entanglement entropy between two free scalar field theories which are interacting with each other in both static and time-dependent ways. We also conjecture a holographic calculation of entanglement entropy between two interacting $\mathcal{N}=4$ super Yang-Mills theories by introducing a minimal surface in the S$^5$ direction, instead of the AdS$_5$ direction. This offers a possible generalization of holographic entanglement entropy.

Figures (7)

• Figure 1: The plot of $s_1(\lambda)$, which is proportional to the entanglement entropy due to the massless interaction for the range $-2<\lambda<2$..
• Figure 2: The replica calculation for the trace $\hbox{Tr}(\rho_{\psi})^n$. We depicted the picture assuming $n=3$.
• Figure 3: A plot of $g_1=\frac{n-1}{n\lambda^2}S^{(n)}_{ent}$ as a function of $t$ in the case of massless interaction. We chose $\epsilon=0.1$.
• Figure 4: A plot of $\frac{n-1}{nC^2}S^{(n)}_{ent}$ in the massive interaction case.
• Figure 5: Geometries of gravity duals for two CFTs (CFT$_1$ and CFT$_2$) with non-vanishing quantum entanglement between them. The surface $\gamma$ denotes the minimal surface which computes the entanglement entropy between them. The upper left picture describes a geometry for two CFTs with massless (or marginal) interactions between them. The upper right one expresses a possibility of geometry with massive interactions, which should be taken cautiously as we mention in section \ref{['fink']}. In this geometry for the massive interactions we need to further identify the two AdS boundaries. These setups should be distinguished from the lower picture, where the two CFTs are entangled without any interactions, such as in the thermofield double construction dual to a AdS black hole.