Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

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.

“…We conclude by noting some of the latest works on the information paradox, as a point of entry into the recent developments [45][46][47][48][49][50][51][52].…”

Section: Jhep08(2021)119mentioning

confidence: 99%

Dirichlet baths and the not-so-fine-grained Page curve

Ghosh

Krishnan

2021

“…It was shown that, like entanglement entropy, capacity could also truly probe the phase transition that happens at the Page time [24,25]. It either shows a peak or changes discontinuously between two phases at Page time, similar in spirit to the subregion complexity [26,27]. Although less familiar, capacity has been studied in condensed matter systems like the Kitaev model, and it appears to be JHEP07(2021)019 well suited for characterizing topologically ordered states [28].…”

Section: Introductionmentioning

confidence: 99%

Capacity of entanglement in local operators

Nandy

2021

Self Cite

We study the time evolution of the excess value of capacity of entanglement between a locally excited state and ground state in free, massless fermionic theory and free Yang-Mills theory in four spacetime dimensions. Capacity has non-trivial time evolution and is sensitive to the partial entanglement structure, and shows a universal peak at early times. We define a quantity, the normalized “Page time”, which measures the timescale when capacity reaches its peak. This quantity turns out to be a characteristic property of the inserted operator. This firmly establishes capacity as a valuable measure of entanglement structure of an operator, especially at early times similar in spirit to the Rényi entropies at late times. Interestingly, the time evolution of capacity closely resembles its evolution in microcanonical and canonical ensemble of the replica wormhole model in the context of the black hole information paradox.

“…The simplest situation corresponds to a twodimensional brane embedded in AdS 3 , as considered in [43] for the study of entanglement entropy. The case of a conformal defect in d dimensions was recently investigated in the context of the island conjecture in relation to subregion complexity [44];…”

Section: Introductionmentioning

confidence: 99%

Volume complexity for Janus AdS3 geometries

Auzzi

Baiguera

Bonansea

et al. 2021

We investigate the complexity=volume proposal in the case of Janus AdS3 geometries, both at zero and finite temperature. The leading contribution coming from the Janus interface is a logarithmic divergence, whose coefficient is a function of the dilaton excursion. In the presence of the defect, complexity is no longer topological and becomes temperature-dependent. We also study the time evolution of the extremal volume for the time-dependent Janus BTZ black hole. This background is not dual to an interface but to a pair of entangled CFTs with different values of the couplings. At late times, when the equilibrium is restored, the couplings of the CFTs do not influence the complexity rate. On the contrary, the complexity rate for the out-of-equilibrium system is always smaller compared to the pure BTZ black hole background.