Massless Entanglement Islands in Cone Holography

TL;DR

This paper extends the concept of entanglement islands to cone holography with massless gravity, demonstrating their existence and analyzing the conditions and features that distinguish it from wedge holography.

Contribution

It generalizes entanglement island analysis to cone holography with DGP terms, revealing new features and confirming the presence of massless gravity and entanglement islands.

Findings

Massless gravity exists on branes in cone holography.

Non-trivial entanglement islands and Page curves are recovered.

Several new features distinguish cone holography from wedge holography.

Abstract

It is controversial whether entanglement islands can exist in massless gravity theories. Recently, it is found that the massless entanglement island appears in wedge holography with DGP gravity on the branes. In this paper, we generalize the discussions to the codim-n holography named cone holography. For simplicity, we focus on the case with a codim-2 E brane and a codim-1 Q brane. We discuss the effective action, mass spectrum and holographic entanglement entropy for cone holography with DGP terms. We verify that there is massless gravity on the branes, and recover non-trivial entanglement islands and Page curves. Besides, we work out the parameter space which allows entanglement islands and Page curves. Compared with wedge holography, there are several new features. First, one can not add DGP gravity on the codim-2 E brane. That is because the energy density has to be a constant on codim-2 branes for Einstein gravity in bulk. Second, the Hartman-Maldacena surface ends only on the codim-1 Q brane. Third, the Hartman-Maldacena surface can be defined only in a finite time. We notice that this unusual situation also appears in AdS/dCFT and even in AdS/CFT. Fortunately, it does not affect the Page curve since it happens after Page time. Our results provide more support that the entanglement island is consistent with massless gravity theories.