# Entanglement islands and braneworlds

One way to seek quantum gravity is to try combining GR and QM. In the 1970s, Hawking argued that this yields the black hole information paradox. Basically, a black hole in his framework should radiate quantum particles entanglement with the interior, but such radiation leads the black hole to evaporate. Information inside of the black hole is then irreversibly lost, in conflict with reversibility expected in quantum theory. The information paradox implies that we are missing something when we simply force GR and QM together.

Recent work using the holographic principle—an unknown aspect of quantum gravity to Hawking in the 70s—has claimed progress towards a resolution using entanglement islands. At sufficiently late times, the emitted radiation becomes redundant with some region inside of the black hole (the island), preventing the paradox. However, one potential issue is that islands have often been found in toy models which are far removed from our own universe. Typically, either the most well-formulated models feature two spacetime dimensions or an "external bath" into which Hawking radiation leaks out. It is debatable whether the island story still provides a resolution when relaxing these limitations.

Across two separate collaborations, I have focused on finding the limits of entanglement islands within the higher-dimensional toy models with baths. I focus specifically on so-called "doubly holographic" models, in which the black hole is taken to reside in a braneworld embedded inside of a spacetime with extra dimensions. These models provide the most tractable setting in which to explore the islands.

Broadly speaking, my work has featured two directions:

Exploring the importance of the bath and its effects on gravity to the relevance of entanglement islands.

Understanding how islands and their role as resolvers of the information paradox may change when deviating from previously explored settings.

# Selected publications

H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas, SS, Jackiw-Teitelboim Gravity from the Karch-Randall Braneworld. Physical Review Letters 129 (2022) 23, 231601. arXiv:2206.04695, preprint June 2022.

We study the effective action of a pair of coupled 2-dimensional braneworlds. We find that subleading quantum fluctuations of the braneworld, controlled by a field known as the radion in the Randall-Sundrum I braneworld, are described by Jackiw-Teitelboim gravity. We also note that the 2-dimensional picture is completely inconsistent with holography if we fail to account for these fluctuations, a result which we had first found back when studying entanglement islands in higher-dimensional versions of this setup in arXiv:2012.04671.

H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas, SS, Entanglement phase structure of a holographic BCFT in a black hole background. Journal of High Energy Physics 05 (2022) 153. arXiv:2112.09132, preprint Dec 2021.

Building on work done in arXiv:2012.04671, we study entanglement islands in a doubly holographic setup where the bath is itself a black hole background. Depending on where we are in parameter space, we see that the information either changes in time (but in a way that does not lead to an information paradox) or remains constant in time. This peculiar phase structure is numerically specified.

H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas, SS, Inconsistency of islands in theories with long-range gravity. Journal of High Energy Physics 01 (2022) 182. arXiv:2107.03390, preprint Jul 2021.

We argue that there exist puzzles regarding entanglement islands in massless gravity. Specifically, we discuss how the information represented by the island cannot be equated to information on the boundary due to the usual constraints of gravity. This is not an issue when gravity is massive, however, which is why the doubly holographic models work.

E. Caceres, A. Kundu, A. K. Patra, SS, Page curves and bath deformations. SciPost Physics Core 5 (2022) 2, 033. arXiv:2107.00022, preprint Jun 2021.

We explore what happens to black hole information in a doubly holographic setup if the bath is slightly "deformed," meaning that we add extra matter which breaks conformal invariance and triggers a renormalization group flow. The main purpose here is to explore whether this impacts the island story. We find that it does on a quantitative level through a robust numerical analysis. This work is a first step towards addressing questions surrounding the potential impact on the island story of having a bath in the first place.

H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas, SS, Information transfer with a gravitating bath. SciPost Physics 10 (2021) 5, 103. arXiv:2012.04671, preprint Dec 2020.

The typical doubly holographic model features a universe with gravity turned on (a braneworld) coupled to a universe with gravity turned off (the bath). However, we can perform a simple modification to the setup by treating the bath like a braneworld, too. This makes gravity massless again, which is a step towards our own universe. However, we find that the standard story of the information paradox is severely modified; information about the interior is argued to not have any time-dependence.

E. Caceres, A. Kundu, A. K. Patra, SS, Warped information and entanglement islands in AdS/WCFT, Journal of High Energy Physics 07 (2021) 004. arXiv:2012.05425, preprint Dec 2020.

We studied entanglement islands in a different type of holographic setup from AdS/CFT, so as to study how general of a phenomenon the islands are. Notably, our setup here should inherently feature quantum irreversibility (thus allowing for information loss without a paradox), but islands still emerge.

# In progress

H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas, SS, M. Youssef, Swampland bounds on braneworlds from entanglement.

The types of braneworlds studied from Randall--Sundrum-like constructions in AdS gravity furnish effective models of quantum gravity. However, we know that such effective theories should be constrained by UV physics, and exploring these constraints falls under the realm of the swampland program. The AdS/CFT dictionary comes from the underlying string theory and is thus inherently UV in origin, and so we may use its entries to put constraints on the types of branes that can be embedded in AdS. We do so using the Ryu--Takayanagi prescription for entanglement entropy. In particular, we use basic consequences of unitarity and causality to propose constraints on effective braneworld theories. As a test case, we put constraints on RS enhanced by Dvali--Gabadadze--Porrati gravity.