Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDirichlet Baths and the Not-so-Fine-Grained Page Curve
220
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a doubly holographic prescription for computing entanglement entropy on a gravitating brane. It involves a Ryu-Takayanagi surface with a Dirichlet anchoring condition. In braneworld cosmology, a related approach was used previously in arXiv:2007.06551. There, the prescription naturally computed a co-moving entanglement entropy, and was argued to resolve the information paradox for a black hole living in the cosmology. In this paper, we show that the Dirichlet prescription leads to reasonable results, when applied to a recently studied wedge holography set up with a gravitating bath. The nature of the information paradox and its resolution in our Dirichlet problem have a natural understanding in terms of the strength of gravity on the two branes and at the anchoring location. By sliding the anchor to the defect, we demonstrate that the limit where gravity decouples from the anchor is continuous -- in other words, as far as island physics is considered, weak gravity on the anchor is identical to no gravity. The weak and (moderately) strong gravity regions on the brane are separated by a Dirichlet wall. We find an intricate interplay between various extremal surfaces, with an island coming to the rescue whenever there is an information paradox. This is despite the presence of massless gravitons in the spectrum. The overall physics is consistent with the slogan that gravity becomes more holographic, as it gets stronger. Our observations strengthen the case that the conventional Page curve is indeed of significance, when discussing the information paradox in flat space. We work in high enough dimensions so that the graviton is non-trivial, and our results are in line with the previous discussions on gravitating baths in arXiv:2005.02993 and arXiv:2007.06551.
rate research
Read More
Asymptotic Causal Diamonds (ACDs) are a natural flat space analogue of AdS causal wedges, and it has been argued previously that they may be useful for understanding bulk locality in flat space holography. In this paper, we use ACD-inspired ideas to argue that there exist natural candidates for Quantum Extremal Surfaces (QES) and entanglement wedges in flat space, anchored to the conformal boundary. When there is a holographic screen at finite radius, we can also associate entanglement wedges and entropies to screen sub-regions, with the system naturally coupled to a sink. The screen and the boundary provide two complementary ways of formulating the information paradox. We explain how they are related and show that in both formulations, the flat space entanglement wedge undergoes a phase transition at the Page time in the background of an evaporating Schwarzschild black hole. Our results closely parallel recent observations in AdS, and reproduce the Page curve. That there is a variation of the argument that can be phrased directly in flat space without reliance on AdS, is a strong indication that entanglement wedge phase transitions may be key to the information paradox in flat space as well. Along the way, we give evidence that the entanglement entropy of an ACD is a well-defined, and likely instructive, quantity. We further note that the picture of the sink we present here may have an understanding in terms of sub-matrix deconfinement in a large-$N$ setting.
We consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the RT/HRT surfaces in the higher-dimensional theory. Using this we compute the entropy of Hawking radiation and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes. The higher-dimensional geometry connects the radiation to the black hole interior in the spirit of ER=EPR. The black hole interior then becomes part of the entanglement wedge of the radiation. Inspired by this, we propose a new rule for computing the entropy of quantum systems entangled with gravitational systems which involves searching for islands in determining the entanglement wedge.
Quantum corrections to the entanglement entropy of matter fields interacting with dynamical gravity have proven to be very important in the study of the black hole information problem. We consider a one-particle excited state of a massive scalar field infalling in a pure AdS$_3$ geometry and compute these corrections for bulk subregions anchored on the AdS boundary. In the dual CFT$_2$, the state is given by the insertion of a local primary operator and its evolution thereafter. We calculate the area and bulk entanglement entropy corrections at order $mathcal{O}(N^0)$, both in AdS and its CFT dual. The two calculations match, thus providing a non-trivial check of the FLM formula in a dynamical setting. Further, we observe that the bulk entanglement entropy follows a Page curve. We explain the precise sense in which our setup can be interpreted as a simple model of black hole evaporation and comment on the implications for the information problem.
Recent developments on black holes have shown that a unitarity-compatible Page curve can be obtained from an ensemble-averaged semi-classical approximation. In this paper, we emphasize (1) that this peculiar manifestation of unitarity is not specific to black holes, and (2) that it can emerge from a single realization of an underlying unitary theory. To make things explicit, we consider a hard sphere gas leaking slowly from a small box into a bigger box. This is a quantum chaotic system in which we expect to see the Page curve in the full unitary description, while semi-classically, eigenstates are expected to behave as though they live in Berrys ensemble. We reproduce the unitarity-compatible Page curve of this system, semi-classically. The computation has structural parallels to replica wormholes, relies crucially on ensemble averaging at each epoch, and reveals the interplay between the multiple time-scales in the problem. Working with the ensemble averaged $state$ rather than the entanglement entropy, we can also engineer an information paradox. Our system provides a concrete example in which the ensemble underlying the semi-classical Page curve is an ergodic proxy for a time average, and not an explicit average over many theories. The questions we address here are logically independent of the existence of horizons, so we expect that semi-classical gravity should also be viewed in a similar light.
Whether what you see in Figure 1 is a flamingo or a bird, is the question we ask in this paper. While fine-grained visual classification (FGVC) strives to arrive at the former, for the majority of us non-experts just bird would probably suffice. The real question is therefore -- how can we tailor for different fine-grained definitions under divergent levels of expertise. For that, we re-envisage the traditional setting of FGVC, from single-label classification, to that of top-down traversal of a pre-defined coarse-to-fine label hierarchy -- so that our answer becomes bird-->Phoenicopteriformes-->Phoenicopteridae-->flamingo. To approach this new problem, we first conduct a comprehensive human study where we confirm that most participants prefer multi-granularity labels, regardless whether they consider themselves experts. We then discover the key intuition that: coarse-level label prediction exacerbates fine-grained feature learning, yet fine-level feature betters the learning of coarse-level classifier. This discovery enables us to design a very simple albeit surprisingly effective solution to our new problem, where we (i) leverage level-specific classification heads to disentangle coarse-level features with fine-grained ones, and (ii) allow finer-grained features to participate in coarser-grained label predictions, which in turn helps with better disentanglement. Experiments show that our method achieves superior performance in the new FGVC setting, and performs better than state-of-the-art on traditional single-label FGVC problem as well. Thanks to its simplicity, our method can be easily implemented on top of any existing FGVC frameworks and is parameter-free.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
