We study the motion of a string in the background of the Schwarzschild black hole in AdS_5 by applying the standard arsenal of dynamical systems. Our description of the phase space includes: the power spectrum, the largest Lyapunov exponent, Poincare sections and basins of attractions. We find convincing evidence that the motion is chaotic. We discuss the implications of some of the quantities associated with chaotic systems for aspects of the gauge/gravity correspondence. In particular, we suggest some potential relevance for the information loss paradox.
The aim of this note is to explore Susskind's proposal [arXiv:1802.01198] on the connection between operator size in chaotic theories and the bulk momentum of a particle falling into black holes (see also [arXiv:1804.04156, 1806.05574, 1904.12819, 1912.05996, 2006.03019] for more recent generalizations), in a broad class of models involving Gauss-Bonnet(GB) and Lifshitz-Hyperscaling violating theories in AdS. For Gauss-Bonnet black holes, the operator size is seen to be suppressed as the coupling constant $λ$ is increased. For the Lifshitz-hyperscaling violating theories characterised by the p…
In this paper we explore the correspondence between four-dimensional Born-Infeld theory and five-dimensional classical gravity. The Born-Infeld theory side corresponds to the low energy effective theory for open strings ending on coincident D3-branes in a (slowly varying) background Kalb-Ramond field, including all higher-derivative corrections. On the gravity side one has the gravitational (closed string) description of D3-branes in the same background Kalb-Ramond field and the correspondence is thus a consequence of the open/closed string duality. According to the correspondence the gravity …
We study a geometrical representation of the quantum information metric in the gauge/gravity correspondence. We consider the quantum information metric that measures the distance between the ground states of two theories on the field theory side, one of which is obtained by perturbing the other. We show that the information metric is represented by a back reaction to the volume of a codimension-2 surface on the gravity side if the unperturbed field theory possesses the Poincare symmetry.
We identify the spectral properties of Hawking-Unruh radiation in the eternal black hole at ultra low energies as a probe for the chaotic level statistics of quantum black holes. Level repulsion implies that there are barely Hawking particles with an energy smaller than the level separation. This effect is experimentally accessible by probing the Unruh heat bath with a linear detector. We provide evidence for this effect via explicit and exact calculations in JT gravity building on a radar definition of bulk observables in the model. Similar results are observed for the bath energy density. Th…
We discuss $SL(N,\mathbb{C})$ Chern-Simons higher spin gauge theories in Euclidean AdS$_3$. With appropriate boundary term, we derive the higher spin generalization of Schwarzian on-shell action. We investigate gravitationally dressed bi-locals, and we study the soft higher spin mode expansion to obtain soft mode eigenfunctions. We also derive the spin-$s$ eigenfunction from $\mathcal{W}$-Ward identity and a recursion relation. Using the on-shell action, we evaluate the contributions of the soft higher spin modes to the out-of-time-order correlators, and the corresponding Lyapunov exponent of …
Gravity/Non-Commutative Yang-Mills Correspondence and Doubletons
本文讨论了非对易Yang-Mills理论的引力对偶描述，在对易极限下，该引力对偶描述约化为AdS_{5} x S_{5}的引力对偶描述.结果发现，在这种对偶引力描述中，除非取交换极限，否则双重态不解耦。在AdS_{5}空间中的二重态的退耦意味着对偶规范理论具有SU（N）规范对称性。我们的结果意味着这种引力描述与非对易U（N）规范理论是对偶的。这与非对易U（N）规范理论中U（1）和SU（N）规范对称性不可分离的观点是一致的。
Wilson loops in (p+1)-dimensional Yang-Mills theories using gravity/gauge theory correspondence
利用引力/规范理论对应，计算了（p+1）维Yang-Mills理论强耦合等离子体中类时和类光威尔逊圈的期望值.由类时威尔逊圈得到了偶极以任意速度0<v 1穿过等离子体时的速度相关夸克-反夸克势<1 and also obtain expressions for the screening lengths. When the velocity v-->，威尔逊圈变为类光，并得到了强耦合等离子体中喷流猝灭参数的形式。
On the Gauge/Gravity Correspondence and the Open/Closed String Duality
在这篇文章中，我们审查的规范/重力对应的有效性在超对称和非超对称弦模型的条件。我们首先回顾一下IIB型理论在轨道折叠C^2/Z_2和C^3/（Z_2 x Z_2）上发生了什么，在这些轨道上，这种对应非常好。在这些情况下，通过对D3膜之间的相互作用进行一个完整的弦计算，已经表明这种对应起作用的事实是开/闭对偶和缺乏阈值校正的结果。然后，我们回顾了0型理论的建设，其orbifolds和orientifolds具有开放和封闭弦快子的光谱，对于这样的模型，我们研究了规范/引力对应的有效性，得出的结论是，这不是一个特殊的超对称理论，但它也可能适用于非超对称模型。同样在这些情况下，当它起作用时，它又是开/闭弦对偶和消失阈值修正的结果。
We studied the canonical structure of 2D $F(R)$ gravity. Its equivalence with Jackiw-Teitelboim gravity is demonstrated when no matter presents. Then, due to AdS$_2$/CFT$_1$ correspondence, such $F(R)$ gravity is equivalent to the Sachdev-Ye--Kitaev models. The singular $D\to 2$ limit of $F(R)$ gravity is also studied. It is shown that in such a limit AdS$_2$/CFT$_1$ correspondence is not realized.
We show that the so-called chaos bound, proposed by Maldacena, Shenker, and Stanford, can be violated in $f(T)$ teleparallel gravity. In particular, it is possible to select a new gravitational Lyapunov parameter, controlling chaotization of circular trajectories, in black hole photo-sphere, that can exceed the Maldacena, Shenker and Stanford thermal bound. This feature alters the standard quasi-normal modes and ringdown phase after black hole merging with intriguing implications for future gravitational wave detections and black hole shadow measurements. It is a general characteristic for sev…
We study quantum chaos of rotating BTZ black holes in Topologically Massive gravity (TMG). We discuss the relationship between chaos parameters including Lyapunov exponents and butterfly velocities from shock wave calculations of out-of-time-order correlators (OTOC) and from pole-skipping analysis. We find a partial match between pole-skipping and the OTOC results in the high temperature regime. We also find that the velocity bound puts a chaos constraint on the gravitational Chern-Simons coupling.
We show that several features of the Jackiw-Teitelboim model are in fact universal properties of two-dimensional Maxwell-dilaton gravity theories with a broad class of asymptotics. These theories satisfy a flow equation with the structure of a dimensionally reduced TTbar deformation, and exhibit chaotic behavior signaled by a maximal Lyapunov exponent. One consequence of our results is a no-go theorem for smooth flows from an asymptotically AdS2 region to a de Sitter fixed point.
In this work, a correspondence between black hole solutions of conformal and massive theories of gravity is found. It is seen that this correspondence imposes some constraints on parameters of these theories. What is more, a relation between the mass of black holes and the parameters of massive gravity is found. Indeed, the acceptable ranges of massive gravity parameters ($c_{1}$\ and $c_{2}$) are found. It is shown that by considering the positive mass of black holes, some ranges of $c_{1}$\ and $c_{2}$ are acceptable.
The fluid/gravity correspondence establishes how gravitational dynamics, as dictated by Einstein's field equations, are related to the fluid dynamics, governed by the relativistic Navier-Stokes equations. In this work the correspondence is extended, where the duality between incompressible fluids and gravitational backgrounds with soft hair excitations is implemented. This construction is set through appropriate boundary conditions to the gravitational background, leading to a correspondence between generalized incompressible Navier-Stokes equations and soft hairy horizons.
We consider fluid/gravity correspondence in a general rotating black hole background with scalar and electromagnetic fields. Using the method of Petrov-like boundary condition, we show that the scalar and the electromagnetic fields contribute external forces to the dual Navier-Stokes equation and the rotation of black hole induces the Coriolis force.
In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a timelike hypersurface, we find that the perturbation effects of massive gravity in bulk can be completely governed by the incompressible Navier-Stokes equation living on the cutoff surface under the near horizon and nonrelativistic limits. Furthermore, we have concisely computed the ratio of dynamical viscosity to entropy density for two massive Einstein gra…
We consider the lower bound for the shear viscosity-to-entropy density ratio, obtained from the fluid/gravity correspondence, in order to constrain the post-Newtonian parameter of brane-world metrics. In particular, we analyse the Casadio-Fabbri-Mazzacurati (CFM) effective solutions for the gravity side of the correspondence and argue that including higher order terms in the hydrodynamic expansion can lead to a full agreement with the experimental bounds, for the Eddington-Robertson-Schiff post-Newtonian parameter in the CFM metrics. This lends further support to the physical relevance of the …
We discuss the emergence of black hole shadow and photon-sphere in the context of $f(R)$ gravity. It is shown that the shadow is exponentially sensitive to linear instabilities of metric coming from some $f(R)$ solutions. Thus, the instabilities of photon circular trajectories, delimiting the black hole photon-sphere, are double exponentialized. Specifically we individuate two Lyapunov exponents, rather than only one, related to two different sources of chaos in geodesic orbits as a sort of butterfly effect. Such a result violates the black hole chaos bound proposed by Maldacena, Shenker and S…
Freelance Fluid/Gravity Correspondence, 3d Analysis
School of Physics, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）；Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院）
We consider (1+1)-dimensional dilaton gravity with a reflecting dynamical boundary. The boundary cuts off the region of strong coupling and makes our model causally similar to the spherically-symmetric sector of multidimensional gravity. We demonstrate that this model is exactly solvable at the classical level and possesses an on-shell SL(2,R) symmetry. After introducing general classical solution of the model, we study a large subset of soliton solutions. The latter describe reflection of matter waves off the boundary at low energies and formation of black holes at energies above critical. Th…
