Holographic entanglement entropy probes (non)locality

TL;DR

The paper investigates how built-in nonlocality in strongly coupled theories alters entanglement entropy, using the holographic Ryu–Takayanagi framework. It analyzes Little String Theory and Noncommutative Yang–Mills: both exhibit a short-distance volume-law regime, transitioning to an area law in the infrared, with LST featuring a tube geometry and UV–IR matching, while NCYM shows strong UV/IR mixing and orientation-dependent behavior. A key insight is that Lorentz symmetry tends to enforce the area law for field-theory densities of states, rendering volume-law entanglement a diagnostic of nonlocality and/or Lorentz violation. These results provide nonperturbative benchmarks for locality versus nonlocality in holographic entanglement, and highlight how UV completions and open-string metrics shape entanglement scaling. The study also emphasizes the role of UV/IR mixing and the density of states in governing the leading short-distance entanglement structure.

Abstract

We study the short-distance structure of geometric entanglement entropy in certain theories with a built-in scale of nonlocality. In particular we examine the cases of Little String Theory and Noncommutative Yang-Mills theory, using their AdS/CFT descriptions. We compute the entanglement entropy via the holographic ansatz of Ryu and Takayanagi to conclude that the area law is violated at distance scales that sample the nonlocality of these models, being replaced by an extensive volume law. In the case of the noncommutative model, the critical length scale that reveals the area/volume law transition is strongly affected by UV/IR mixing effects. We also present an argument showing that Lorentz symmetry tends to protect the area law for theories with field-theoretical density of states.

Figures (8)

• Figure 1: The different regions of the bulk type IIA background. The local string coupling grows towards smaller radii in the NS5 'tube', becoming of $O(1)$ at $r\sim r_s = g_s R$. At lower radii the system is well approximated by the uplifted solution to eleven dimensions, i.e. the smeared ${\widetilde{\rm M5}}$-brane solution, which localizes below $r\sim r_H = g_s R /\sqrt{N}$ and flows to the ${\rm AdS}_7 \times {\bf S}^4$ dual of the $(2,0)$ CFT in six dimensions. In the type IIB case, the ${\widetilde{\rm M5}}$ phase is replaced by the near-horizon D5-brane background, and the matching at $r\sim r_H$ takes the system to a non-geometrical phase described by weakly-coupled Yang--Mills theory.
• Figure 2: Schematic plot of the UV/IR relation, as determined by the toy minimal hypersurfaces of capped cylinders for a given value of $\ell$, versus the location of the turning point in the bulk. For $\ell > \ell_H$ we have the standard 'Heisenberg-type' relation $\ell(u_*) \sim 1/u_*$, characteristic of local theories. In the interval $\ell_c < \ell < \ell_H$ the minimal surface is stuck at $u_* = u_H = T_H$ (the IR end of the tube). At $\ell=\ell_c$ there is a degenerate set of minimal surfaces with turning points anywhere in the tube, and finally for $\ell < \ell_c$ the only minimal surface is the one set at the cutoff scale $z=z_\varepsilon$.
• Figure 3: Schematic plot of the entropy density $s[\ell] = S[A] / |\partial A|$ for the toy minimal hypersurfaces of capped cylinders showing the local regime at $\ell \geq \ell_H$, the nonlocal volume law at $\ell < \ell_H$ and the intermediate transient.
• Figure 4: Schematic picture of the background profile in IIA deconstruction, showing the different regions of interest in the vicinity of the LST regime.
• Figure 5: Schematic plot of $\ell$ as a function of $r_*$, $\rho_*$ for the deconstructed LST background. In the tube region $r_H < r < r_\theta$ one has a constant behavior of $\ell$ as well as in $r_\theta < r < r_\Lambda$, whereas for the corresponding regions of $\ell > \ell_c$ and $\ell < \ell_\theta$ one has $\ell \sim \rho_*^{-\frac{1}{2}}$.