arXiv subjects

Rong-Xin Miao

Publications and source records attributed to Rong-Xin Miao.

At least 55 records · Page 3Linked to original sources

arXiv2019

Holographic BCFT with Dirichlet Boundary Condition

Neumann boundary condition plays an important role in the initial proposal of holographic dual of boundary conformal field theory, which has yield many interesting results and passed several non-trivial tests. In this paper, we show that Dirichlet boundary condition works as well as Neumann boundary condition. For instance, it includes AdS solution and obeys the g-theorem. Furthermore, it can produce the correct expression of one point function, the boundary Weyl anomaly and the universal relations between them. We also study the relative boundary condition for gauge fields, which is the counterpart of Dirichlet boundary condition for gravitational fields. Interestingly, the four-dimensional Reissner-Nordstrom black hole with magnetic charge is an exact solution to relative boundary condition under some conditions. This holographic model predicts that a constant magnetic field in the bulk can induce a constant current on the boundary in three dimensions. We suggest to measure this interesting boundary current in materials such as the graphene.

hep-th↗

arXiv2018

Weyl Anomaly Induced Current in Boundary Quantum Field Theories

We show that when an external magnetic field parallel to the boundary is applied, the Weyl anomaly gives rises to a new anomalous current in the vicinity of the boundary. The induced current is a magnetization current in origin: the movement of the virtual charges near the boundary give rise to a nonuniform magnetization of the vacuum and hence a magnetization current. Unlike other previously studied anomalous current phenomena such as the chiral magnetic effect or the chiral vortical effect, this induced current does not rely on the presence of a material system and can occur in vacuum. Similar to the Casimir effect, our discovered phenomenon arises from the effect of the boundary on the quantum fluctuations of the vacuum. However this induced current is purely quantum mechanical and has no classical limit. We briefly comment on how this induced current may be observed experimentally.

hep-th↗

arXiv2018

Anomalous Transport in Holographic Boundary Conformal Field Theories

Recently, it is found that when an external magnetic field parallel to the boundary is applied, Weyl anomaly gives rises to a new anomalous current transport in the vicinity of the boundary. At the leading order of closeness from the boundary, the current is determined universally by the central charge of the theory. In this paper, we give a holographic proof for the existence and universality for this transport phenomena. We show that the current is independent of boundary conditions in four dimensions while it depends on boundary conditions in other dimensions. We also study the backreaction of the bulk Maxwell fields on the AdS spacetime and obtain the holographic Weyl anomaly for 5d BCFTs in presence of the background field strength.

hep-th↗

arXiv2018

Universality for Shape Dependence of Casimir Effects from Weyl Anomaly

We reveal elegant relations between the shape dependence of the Casimir effects and Weyl anomaly in boundary conformal field theories (BCFT). We show that for any BCFT which has a description in terms of an effective action, the near boundary divergent behavior of the renormalized stress tensor is completely determined by the central charges of the theory. These relations are verified by free BCFTs. We test them with holographic models of BCFT and find exact agreement. We propose that these relations between Casimir coefficients and central charges hold for any BCFT. With the holographic models, we reproduce not only the precise form of the near boundary divergent behavior of the stress tensor, but also the surface counter term that is needed to make the total energy finite. As they are proportional to the central charges, the near boundary divergence of the stress tensor must be physical and cannot be dropped by further artificial renormalization.Our results thus provide affirmative support on the physical nature of the divergent energy density near the boundary, whose reality has been a long-standing controversy in the literature.

hep-th↗

arXiv2017

Maximally Entangled State and Bell's Inequality in Qubits

A maximally entangled state is a quantum state which has maximum von Neumann entropy for each bipartition. Through proposing a new method to classify quantum states by using concurrences of pure states of a region, one can apply Bell's inequality to study intensity of quantum entanglement of maximally entangled states. We use a class of seven-qubit quantum states to demonstrate the method, where we express all coefficients of the quantum states in terms of concurrences of pure states of a region. When a critical point of an upper bound of Bell's inequality occurs in our quantum states, one of the quantum state is a ground state of the toric code model on a disk manifold. Our result also implies that the maximally entangled states does not suggest local maximum quantum entanglement in our quantum states.

quant-ph↗

arXiv2017

On New Proposal for Holographic BCFT

This paper is an extended version of our short letter on a new proposal for holographic boundary conformal field, i.e., BCFT. By using the Penrose-Brown-Henneaux (PBH) transformation, we successfully obtain the expected boundary Weyl anomaly. The obtained boundary central charges satisfy naturally a c-like theorem holographically. We then develop an approach of holographic renormalization for BCFT, and reproduce the correct boundary Weyl anomaly. This provides a non-trivial check of our proposal. We also investigate the holographic entanglement entropy of BCFT and find that our proposal gives the expected orthogonal condition that the minimal surface must be normal to the spacetime boundaries if they intersect. This is another support for our proposal. We also find that the entanglement entropy depends on the boundary conditions of BCFT and the distance to the boundary; and that the entanglement wedge behaves a phase transition, which is important for the self-consistency of AdS/BCFT. Finally, we show that the proposal of arXiv:1105.5165 is too restrictive that it always make vanishing some of the boundary central charges.

hep-th↗

arXiv2017

A New Proposal for Holographic BCFT

We propose a new holographic dual of conformal field theory defined on a manifold with boundaries, i.e. BCFT. Our proposal can apply to general boundaries and agrees with arXiv:1105.5165 for the special case of a disk and half plane. Using the new proposal of AdS/BCFT, we successfully obtain the expected boundary Weyl anomaly and the obtained boundary central charges satisfy naturally a c-like theorem holographically. We also investigate the holographic entanglement entropy of BCFT and find that the minimal surface must be normal to the bulk spacetime boundaries when they intersect. Interestingly,the entanglement entropy depends on the boundary conditions of BCFT and the distance to the boundary. The entanglement wedge has an interesting phase transition which is important for the self-consistency of AdS/BCFT.

hep-th↗

arXiv2016

Universality in the Shape Dependence of Holographic Rényi Entropy for General Higher Derivative Gravity

We consider higher derivative gravity and obtain universal relations for the shape coefficients $(f_a, f_b, f_c)$ of the shape dependent universal part of the Rényi entropy for four dimensional CFTs in terms of the parameters $(c, t_2, t_4)$ of two-point and three-point functions of stress tensors. As a consistency check, these shape coefficients $f_a$ and $f_c$ satisfy the differential relation as derived previously for the Rényi entropy. Interestingly, these holographic relations also apply to weakly coupled conformal field theories such as theories of free fermions and vectors but are violated by theories of free scalars. The mismatch of $f_a$ for scalars has been observed in the literature and is due to certain delicate boundary contributions to the modular Hamiltonian. Interestingly, we find a combination of our holographic relations which are satisfied by all free CFTs including scalars. We conjecture that this combined relation is universal for general CFTs in four dimensional spacetime. Finally, we find there are similar universal laws for holographic Rényi entropy in general dimensions.

hep-th↗

arXiv2015

Generalized Gravitational Entropy from Total Derivative Action

We investigate the generalized gravitational entropy from total derivative terms in the gravitational action. Following the method of Lewkowycz and Maldacena, we find that the generalized gravitational entropy from total derivatives vanishes. We compare our results with the work of Astaneh, Patrushev, and Solodukhin. We find that if total derivatives produced nonzero entropy, the holographic and the field-theoretic universal terms of entanglement entropy would not match. Furthermore, the second law of thermodynamics could be violated if the entropy of total derivatives did not vanish.

hep-th↗

arXiv2015

Universal Terms of Entanglement Entropy for 6d CFTs

We derive the universal terms of entanglement entropy for 6d CFTs by applying the holographic and the field theoretical approaches, respectively. Our formulas are conformal invariant and agree with the results of [34,35]. Remarkably, we find that the holographic and the field theoretical results match exactly for the $C^2$ and $Ck^2$ terms. Here $C$ and $k$ denote the Weyl tensor and the extrinsic curvature, respectively. As for the $k^4$ terms, we meet the splitting problem of the conical metrics. The splitting problem in the bulk can be fixed by equations of motion. As for the splitting on the boundary, we assume the general forms and find that there indeed exists suitable splitting which can make the holographic and the field theoretical $k^4$ terms match. Since we have much more equations than the free parameters, the match for $k^4$ terms is non-trivial.

hep-th↗

arXiv2015

A holographic proof of the universality of corner entanglement for CFTs

There appears a universal logarithmic term of entanglement entropy, i.e., $-a(Ω) \log(H/δ)$, for 3d CFTs when the entangling surface has a sharp corner. $a(Ω)$ is a function of the corner opening angle and behaves as $a(Ω\to π)\simeq σ(π-Ω)^2$ and $a(Ω\to 0)\simeq κ/Ω$, respectively. Recently, it is conjectured that $σ/C_T=π^2/24 $, where $C_T$ is central charge in the stress tensor correlator, is universal for general CFTs in three dimensions. In this paper, by applying the general higher curvature gravity, we give a holographic proof of this conjecture. We also clarify some interesting problems. Firstly, we find that, in contrast to $σ/C_T$, $κ/C_T$ is not universal. Secondly, the lower bound $a_E(Ω)/C_T$ associated to Einstein gravity can be violated by higher curvature gravity. Last but not least, we find that there are similar universal laws for CFTs in higher dimensions. We give some holographic tests of these new conjectures.

hep-th↗

arXiv2015

A note on the resolution of the entropy discrepancy

It was found by Hung, Myers and Smolkin that there is entropy discrepancy for the CFTs in 6-dimensional space-time, between the field theoretical and the holographic analysis. Recently, two different resolutions to this puzzle have been proposed. One of them suggests to utilize the anomaly-like entropy and the generalized Wald entropy to resolve the HMS puzzle, while the other one initiates to use the entanglement entropy which arises from total derivative terms in the Weyl anomaly to explain the HMS mismatch. We investigate these two proposals carefully in this note. By studying the CFTs dual to Einstein gravity, we find that the second proposal can not solve the HMS puzzle. Moreover, the Wald entropy formula is not well-defined on horizon with extrinsic curvatures, in the sense that, in general, it gives different results for equivalent actions.

hep-th↗

arXiv2015

Holographic Entanglement Entropy for the Most General Higher Derivative Gravity

The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the `anomaly of entropy' of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.

hep-th↗

arXiv2015

Entropy for gravitational Chern-Simons terms by squashed cone method

In this paper we investigate the entropy of gravitational Chern-Simons terms for the horizon with non-vanishing extrinsic curvatures, or the holographic entanglement entropy for arbitrary entangling surface. In 3D we find no anomaly of entropy appears. But the squashed cone method can not be used directly to get the correct result. For higher dimensions the anomaly of entropy would appear, still, we can not use the squashed cone method directly. That is becasuse the Chern-Simons action is not gauge invariant. To get a reasonable result we suggest two methods. One is by adding a boundary term to recover the gauge invariance. This boundary term can be derived from the variation of the Chern-Simons action. The other one is by using the Chern-Simons relation $d\bm{Ω_{4n-1}}=tr(\bm{R}^{2n})$. We notice that the entropy of $tr(\bm{R}^{2n})$ is a total derivative locally, i.e. $S=d s_{CS}$. We propose to identify $s_{CS}$ with the entropy of gravitational Chern-Simons terms $Ω_{4n-1}$. In the first method we could get the correct result for Wald entropy in arbitrary dimension. In the second approach, in addition to Wald entropy, we can also obtain the anomaly of entropy with non-zero extrinsic curvatures. Our results imply that the entropy of a topological invariant, such as the Pontryagin term $tr(\bm{R}^{2n})$ and the Euler density, is a topological invariant on the entangling surface.

hep-th↗

arXiv2014

A Note on Holographic Weyl Anomaly and Entanglement Entropy

We develop a general approach to simplify the derivation of the holographic Weyl anomaly. As an application, we derive the holographic Weyl anomaly from general higher derivative gravity in asymptotically $AdS_{5}$ and $AdS_{7}$. Interestingly, to derive all the central charges of 4d and 6d CFTs, we make no use of equations of motion. Following Myers' idea, we propose a formula of holographic entanglement entropy for higher derivative gravity in asymptotically $AdS_5$. Applying this formula, we obtain the correct universal term of entanglement entropy for 4d CFTs. It turns out that our formula is the leading term of Dong's proposal in asymptotically $AdS_5$. Since only the leading term contributes to the universal log term, we actually prove that Dong's proposal yields the correct universal term of entanglement entropy for 4d CFTs. This is a nontrivial test of Dong's proposal.

hep-th↗

arXiv2012

A New Model of Holographic Dark Energy with Action Principle

We propose a new model of holographic dark energy with an action. It is the first time that one can derive a HDE model from the action principle. The puzzles of causality and circular logic about HDE have been completely solved in this model. The evolution of the universe only depends on the present state of the universe, clearly showing that it obeys the law of causality. Furthermore, the use of future event horizon as a present cut-off is not an input but automatically follows from equations of motion. Interestingly, this new model is very similar to the initial one of Li except a new term which may be explained as dark radiation.

hep-th↗

arXiv2012

Einstein Equations From Holographic Thermodynamics and Holographic Entropy

We derive the Einstein field equations and black hole entropy from the first law of thermodynamics on a holographic time-like screen. Because of the universality of gravity, the stress tensor on the screen must be independent of the details of matter fields, so it should be a pure geometric quantity. For simplicity, we assume that the stress tensor on the screen depends on surface Ricci curvature and extrinsic curvature linearly. Then we prove that the surface stress tensor is just the Brown-York stress tensor plus terms which do not affect the field equations of gravitation and the entropy of the system. By assuming a generalized "Fine first law of thermodynamics" or the usual universal first law of thermodynamics on the screen, we can derive the matter field equations as well.

hep-th↗

arXiv2011

Huge Casimir effect at finite temperature in electromagnetic Rindler space

We investigate the Casimir effect at finite temperature in electromagnetic Rindler space, and find the Casimir energy is proportional to $\frac{T^4}{d^2}$ in the high temperature limit, where $T\approx 27 ^\circ\mathrm{C}$ is the temperature and $d\approx 100nm$ is a small cutoff. We propose to make metamaterials to mimic Rindler space and measure the predicted Casimir effect. Since the parameters of metamaterials we proposed are quite simple, this experiment would be easily implemented in laboratory.

physics.optics↗