Entanglement Beyond $\rm AdS$

TL;DR

This work investigates spatial entanglement entropy in a string-theory background that interpolates from $AdS_3$ in the IR to a linear-dilaton UV, dual to a $CFT_2$ deformed by a dimension $(2,2)$ operator. It combines holographic Ryu–Takayanagi calculations with field-theory perturbations of a $T\overline T$-deformed $CFT_2$ to reveal non-local UV features and a Casini–Huerta c-function that remains cutoff-independent and monotone. The large-$L$ entanglement behavior mirrors that of TTbar-deformed theories, while the UV divergence at the minimal length $L_{\min}$ encodes the Hagedorn density of Little String Theory states; finite-temperature generalizations show consistent BTZ-like and linear-dilaton regimes. Overall, the results illuminate how holographic entanglement encodes non-local UV physics and point to avenues for higher-order deformations and related observables.

Abstract

We continue our study of string theory in a background that interpolates between $AdS_3$ in the infrared and a linear dilaton spacetime $R^{1,1}\times R_φ$ in the UV. This background corresponds via holography to a $CFT_2$ deformed by an operator of dimension $(2,2)$. We discuss the structure of spatial entanglement in this model, and compare it to the closely related $T\bar T$ deformed $CFT_2$.

Figures (7)

• Figure 1: The size of the entangling region $L$ as a function of $U_0$ in $\mathcal{M}_3$.
• Figure 2: The background $\mathcal{M}_3$ gives rise at small $U$ to $AdS_3$, and at large $U$ to a linear dilaton background. The two are smoothly connected at $U\sim{1\over\sqrt{k}}$. For large $L$ the bottom of the minimal RT surface is deep inside the $AdS_3$ region (red curve), while for $L\sim L_{\rm min}$ it is in the linear dilaton region (blue curve). The properties of the corresponding entanglement entropy are accordingly different.
• Figure 3: $S_{EE}(L)$.
• Figure 4: $C(L)$.
• Figure 5: $C'(L)$.