A traversable wormhole generally violates the averaged null energy condition, typically requiring exotic matter. Recently, it was discovered that a traversable wormhole can be realized with non-exotic matter in Einstein-Dirac-Maxwell theories in flat space. This study extends the discussion to AdS spacetime and finds traversable wormholes with spherical and planar topologies. Furthermore, based on the AdS/CFT correspondence, we compute the entanglement entropy of strips and disks on the two AdS boundaries of the wormhole. We find that the entanglement entropy undergoes a phase transition as the subsystem size increases.

China

Hua-Chao Liu

Rong-Xin Miao

Traversable wormholes in AdS and entanglement * Supported by the National Natural Science Foundation of China (12275366)

We propose that the quantum states of black hole responsible for the Bekenstein-Hawking entropy are given by a thin shell of Bell particles located at the region just underneath the horizon. We argue that the configuration can be stabilized by a new kind of degeneracy pressure which is suggested by a noncommutative geometry in the interior of the black hole. Black hole singularity is avoided. We utilize the work of Parikh and Wilczek <cross-ref refid='br0010' id='crf0060'>[1]</cross-ref> to include the effect of tunneling on the Bell particles. We show that partially tunneled Bell particles give the Page curve of Hawking radiation, and the entirety of information initially stored in the black hole is returned to the outside via the Hawking radiation. In view of entropic force, the location of these Bell states is naturally related to the island and the quantum extremal surface.

Taiwan

Chong-Sun Chu

Tunneling of Bell particles, page curve and black hole information

Recently, it has been proposed that holography imposes a universal lower bound on the Casimir effect for 3d BCFTs. This paper generalizes the discussions to higher dimensions. We find Einstein gravity, DGP gravity, and Gauss-Bonnet gravity sets a universal lower bound of the strip Casimir effect in general dimensions. We verify the holographic bound by free theories and $\textit{O}$($\textit{N}$) models in the $\textit{ϵ}$ expansions. We also derive the holographic bound of the Casimir effect for a wedge and confirm free theories obey it. It implies holography sets a lower bound of the Casimir effect for general boundary shapes, not limited to the strip. Finally, we briefly comment on the impact of mass and various generalizations and applications of our results.

Holographic bound of Casimir effect in general dimensions

Due to the splitting problem, it is difficult to derive the holographic entanglement entropy for general higher derivative gravity. Inspired by double holography and renormalized entanglement entropy, we develop a method to derive the generalized gravitational entropy for the brane-world higher derivative (BWHD) gravity. Remarkably, this approach is independent of the splitting problem. The so-called BWHD gravity is an effective theory on the brane, given by the counter terms of holographic renormalization. Interestingly, all solutions to Einstein gravity are also solutions to BWHD gravity. We first verify our approach can derive the correct results for curvature-squared gravity and then derive the holographic entanglement entropy for cubic BWHD gravity, which is the main result of this paper. We also derive the entropy of quartic BWHD gravity in flat space with constant extrinsic curvatures and perform several tests on our results. Finally, we briefly comment on our results.

Zi-Bing Xie

Holographic entanglement entropy for brane-world higher derivative gravity

We propose a quantum model of the Schwarzschild black hole as a quantum mechanics of a system of fermionic degrees of freedom. The system has a constant density of states and a Fermi energy that is inversely proportional to the size of the system. Assuming the equivalence principle, we show that the degeneracy pressure of the Fermi degrees of freedom is able to withstand the collapse of gravity if the radius of the system is given precisely by the horizon radius of the Schwarzschild black hole. In our model, the fermionic degrees of freedom at each energy level can be entangled in certain different ways, giving rise to a multitude of degenerate ground states of the system. The counting of these microstates reproduces precisely the Bekenstein-Hawking entropy. This simple Fermi model is universal and works also for the Reissner-Nordström charged black hole as well as black holes with a cosmological constant. From the properties of the Fermi variables, we propose that quantum gravity is characterized by a principle of maximal capacity of states where there can be no more than <math><mi>V</mi><mo>/</mo><msubsup><mi>l</mi><mi>P</mi><mn>3</mn></msubsup></math> quantum states in any volume <math><mi>V</mi></math>. It implies a loss of spatial locality below the Planck length and suggests that any singularity predicted by general relativity is resolved and replaced by a quantum space in quantum gravity. In our model, a black hole spacetime is equipped with a uniform distribution of energy levels. This is another reason why black holes can be considered a simple harmonic oscillator of quantum gravity.

Fermi model of a quantum black hole

This paper investigates the Casimir effect of a wedge and its holographic dual. We prove that the displacement operator universally determines the wedge Casimir effect in the smooth limit. Besides, we argue that the wedge Casimir energy increases with the opening angle and test it with several examples. Furthermore, we construct the holographic dual of wedges in AdS/BCFT in general dimensions. We verify that our proposal can produce the expected Casimir effect within smooth and singular limits. We observe that the Casimir energy density of a wedge increases with the brane tension. Next, we discuss the wedge contribution to holographic entanglement entropy and find it increases with the opening angle, similar to the wedge Casimir energy. Finally, we briefly discuss the holographic polygon in AdS3/BCFT2 and its generalization to higher dimensions.

Casimir effect and holographic dual of wedges

This paper investigates the brane-localized interactions, including DGP gravity and higher derivative (HD) gravity localized on the brane. We derive the effective action on the brane, which suggests the brane-localized HD gravity suffers the ghost problem generally. Besides, we obtain novel algebraic identities of the mass spectrum, which reveal the global nature and can characterize the phase transformation of the mass spectrum. We get a powerful ghost-free condition from the spectrum identities, which rules out one type of brane-localized HD gravity. We further prove the mass spectrum is real and non-negative m 2 ≥ 0 under the ghost-free condition.

Ghost problem, spectrum identities and various constraints on brane-localized gravity

Cone holography is a codimension-n doubly holographic model, which can be interpreted as the holographic dual of edge modes on defects. The initial model of cone holography is based on mixed boundary conditions. This paper formulates cone holography with Neumann boundary conditions, where the brane-localized gauge fields play an essential role. Firstly, we illustrate the main ideas in an AdS4/CFT1 toy model. We show that the U(1) gauge field on the end-of-the-world brane can make the typical solution consistent with Neumann boundary conditions. Then, we generalize the discussions to general codimension-n cone holography by employing brane-localized p-form gauge fields. We also investigate perturbative solutions and prove the mass spectrum of Kaluza-Klein gravitons is non-negative. Furthermore, we prove that cone holography obeys holographic c-theorem. Finally, inspired by the recently proposed chiral model in AdS/BCFT, we construct another type of cone holography with Neumann boundary conditions by applying massive vector (Proca) fields on the end-of-the-world brane.

Zheng-Quan Cui

Yu Guo

Cone holography with Neumann boundary conditions and brane-localized gauge fields

Entanglement islands play an essential role in the recent breakthrough in addressing the black hole information paradox. Inspired by double holography, it is conjectured that the entanglement islands can exist only in massive gravity. There are many pieces of evidence but also debates for this conjecture. This paper recovers the massless entanglement island in wedge holography with negative DGP gravity on the brane. However, the spectrum of negative DGP gravity includes a massive ghost, implying the model is unstable. Our work supports the view that there is no entanglement island in a well-defined braneworld model of massless gravity if one divides the radiation and black hole regions by minimizing entanglement entropy. However, such a partition results in a zero radiation region containing no information. Whether there are other physical non-trivial partitions of the radiation region is an open question and deserves further study.

Entanglement island versus massless gravity

Because of the Weyl anomaly, the background axial vector field induces novel chiral currents near a boundary. Recently, a non-minimal holographic chiral model has been proposed to produce the expected chiral current. The critical point is adding a boundary mass term <math><msup><mrow><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msup></math> of the axial vector field. This paper investigates the holographic chiral model with general boundary action in AdS/BCFT. We find the nonlinear gauge-violating boundary interactions <math><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msup><mrow><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> generally lead to ghost instability and the singularity problem. On the other hand, the mass term <math><msup><mrow><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msup></math> and gauge-invariant interactions <math><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msup><mrow><mover><mrow><mi>F</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> are free of these issues. For the squared boundary action with mass and kinetic terms, we analyze the holographic chiral current near a boundary. We work out more subleading terms and verify they agree with the field-theoretical results. We find the boundary kinetic term affects only the finite term of chiral currents. Finally, we briefly comment on the applications of our model in cone double holography.