The scrambling time and its delay are calculated using holography in an asymptotically AdS black hole solution of the gauged Einstein-Maxwell-Dilaton-Axion (EMDA) theory, the dyonic Kerr-Sen-AdS$_4$ black hole, perturbed by rotating and charged shock waves along the equator. The leading term of the scrambling time for a black hole with large entropy is logarithmic in the entropy and hence supports the fast scrambling conjecture for this black hole solution, which implies that the system under consideration is chaotic. We also find that the instantaneous minimal Lyapunov index is bounded by $κ=2πT_H/(1-μ\mathcal{L})$, which is analogous to the surface gravity but for the rotating shock waves, and becomes closer to equality for the near extremal black hole. For a small value of the AdS scale, we found that the Lyapunov exponent can exceed the bound for a large value of $\mathcal{L}$. Due to the presence of the electric and magnetic charge of the shock waves, we also show that the scrambling process of this holographic system is delayed by a time scale that depends on the charges of the shock waves. The calculations also hold for the ultra-spinning version of this black hole. The result of this paper generalizes the holographic calculations of chaotic systems which are described by an EMDA theory in the bulk.
We explore some (especially, thermodynamical) properties of the dyonic Kerr-Sen-AdS$_4$ black hole and its ultraspinning counterpart, and check whether or not both black holes satisfy the first law and Bekenstein-Smarr mass formulas. To this end, new Christodoulou-Ruffini-like squared-mass formulae for the usual dyonic Kerr-Sen-AdS$_4$ solution and its ultraspinning cousin are deduced. Similar to the ultraspinning Kerr-Sen-AdS$_4$ black hole case, we demonstrate that the ultraspinning dyonic Kerr-Sen-AdS$_4$ black hole does not always violate the reverse isoperimetric inequality (RII) since th…
Motivated by advanced progress in the holographic theory between rotating black holes and CFT, we explore the conformal invariance on dyonic Kerr-Sen black hole and its gauged family. We consider a neutral massless scalar probe on the black holes' background within the low-frequency limit and exhibit that the solution space possesses $SL(2,R)\times SL(2,R)$ isometry. The periodic identification of the azimuthal angle corresponds to the spontaneous conformal symmetry breaking by temperatures $T_L,T_R$. Using the computation of the central charges on Ref. [25] that we recalculate by considering …
We demonstrate that rotating dyonic black holes in Einstein-Maxwell-Dilaton-Axion (EMDA) theory is holographically dual with 2D conformal field theory. We first investigate the duality on dyonic Kerr-Sen black hole with non-vanishing dilaton and axion charges. The near-horizon geometry of extremal dyonic Kerr-Sen spacetime possesses the $SL(2,R) \times U (1)$ isometry allowing to employ the asymptotic symmetry group method to find the corresponding central charge. We find two different branches of the mass which correspond to CFT with two different central charges $c_L=12am_+$ and $c_L=12am_-$…
Using the Sen's entropy function formalism, we compute the entropy for the extremal dyonic black hole solutions of theories in the presence of dilaton field coupled to the field strength and a dilaton potential. We solve the attractor equations analytically and determine the near horizon metric, the value of the scalar fields and the electric field on the horizon, and consequently the entropy of these black holes. The attractor mechanism plays a very important role for these systems, and after studying the simplest systems involving dilaton fields, we propose a general ansatz for the value of …
In five dimensions, we consider a model described by the Einstein gravity with a source given by a scalar field and various Abelian gauge fields with dilatonic-like couplings. For this model, we are able to construct two dyonic black holes whose three-dimensional horizons are modeled by two nontrivial homogeneous Thurston's geometries. The dyonic solutions are of Lifshitz type with an arbitrary value of the dynamical exponent. In fact, the first gauge field ensures the anisotropy asymptotic while the remaining Abelian fields sustain the electric and magnetic charges. Using the Hamiltonian form…
The notion of information scrambling is tied to the long-time behaviour of a system and therefore is related to its infra-red dynamics. In fast scramblers, information spreads as a logarithmic function of the number of degrees of freedom. Ordinarily, under an RG-flow, scrambling will become faster in the IR since many degrees of freedom are integrated out, as a consequence of the c-theorem. In this article, we consider a class of Holographic quantum field theories (QFT), which are strongly coupled large $N$ gauge theories with large number of adjoint and fundamental matter, in which scrambling…
We study the first law of thermodynamics of dyonic black strings carrying a linear momentum in type IIA string theory compactified on K3 with leading order $α'$ corrections. The low energy effective action contains mixed Chern-Simons terms of the form $-2B_{(2)}\wedge {\rm tr}(R(Γ_\pm)\wedge R(Γ_\pm))$ which is equivalent to $2H_{(3)}\wedge \mathrm{CS}_{(3)}(Γ_\pm)$ up to a total derivative. We find that the naive application of Wald entropy formula leads to two different answers associated with the two formulations of the mixed Chern-Simons terms. Surprisingly, neither of them satisfies the f…
Out-of-time-ordered correlators (OTOCs) have received considerable recent attention as qualitative witnesses of information scrambling in many-body quantum systems. Theoretical discussions of OTOCs typically focus on closed systems, raising the question of their suitability as scrambling witnesses in realistic open systems. We demonstrate empirically that the nonclassical negativity of the quasiprobability distribution (QPD) behind the OTOC is a more sensitive witness for scrambling than the OTOC itself. Nonclassical features of the QPD evolve with timescales that are robust with respect to de…
Random transformations are typically good at "scrambling" information. Specifically, in the quantum setting, scrambling usually refers to the process of mapping most initial pure product states under a unitary transformation to states which are macroscopically entangled, in the sense of being close to completely mixed on most subsystems containing a fraction fn of all n particles for some constant f. While the term scrambling is used in the context of the black hole information paradox, scrambling is related to problems involving decoupling in general, and to the question of how large isolated…
Starting from a metric Ansatz permitting a weak version of Birkhoff's theorem we find static black hole solutions including matter in the form of free scalar and p-form fields, with and without a cosmological constant Λ. Single p-form matter fields permit multiple possibilities, including dyonic solutions, self-dual instantons and metrics with Einstein-Kaelher horizons. The inclusion of multiple p-forms on the other hand, arranged in a homogeneous fashion with respect to the horizon geometry, permits the construction of higher dimensional dyonic p-form black holes and four dimensional axionic …
The delocalization or scrambling of quantum information has emerged as a central ingredient in the understanding of thermalization in isolated quantum many-body systems. Recently, significant progress has been made analytically by modeling non-integrable systems as stochastic systems, lacking a Hamiltonian picture, while honest Hamiltonian dynamics are frequently limited to small system sizes due to computational constraints. In this paper, we address this by investigating the role of conservation laws (including energy conservation) in the thermalization process from an information-theoretic …
One characterization of a chaotic system is the quick delocalization of quantum information (fast scrambling). One therefore expects that in such a system a state quickly becomes locally indistinguishable from its perturbations. In this paper we study the time dependence of the relative entropy between the reduced density matrices of the thermofield double state and its perturbations in two dimensional conformal field theories. We show that in a CFT with a gravity dual, this relative entropy exponentially decays until the scrambling time. This decay is not uniform. We argue that the early time…
We revisit the complexity$=$action proposal for charged black holes. We investigate the complexity for a dyonic black hole, and we find the surprising feature that the late-time growth is sensitive to the ratio between electric and magnetic charges. In particular, the late-time growth rate vanishes when the black hole carries only a magnetic charge. If the dyonic black hole is perturbed by a light shock wave, a similar feature appears for the switchback effect, e.g., it is absent for purely magnetic black holes. We then show how the inclusion of a surface term to the action can put the electri…
We obtain the holographic complexity of an evaporating black hole in the semi-classical RST model of two-dimensional dilaton gravity, using a volume prescription that takes into account the higher-dimensional origin of the model. For classical black holes, we recover the expected late time behaviour of the complexity, but new features arise at the semi-classical level. By considering the volume inside the stretched horizon of the evolving black hole, we obtain sensible results for the rate of growth of the complexity, with an early onset of order the black hole scrambling time followed by an e…
In the context of applications of the AdS/CFT correspondence to condensed matter physics, we compute conductivities for field theory duals of dyonic planar black holes in 3+1-dimensional Einstein-Maxwell-dilaton theories at zero temperature. We combine the near-horizon data obtained via Sen's entropy function formalism with known expressions for conductivities. In this way we express the conductivities in terms of the extremal black hole charges. We apply our approach to three different examples for dilaton theories for which the background geometry is not known explicitly. For a constant scal…
We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the $t = 0$ slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup…
In the corpuscular picture of black hole there exists no geometric notion of horizon which, instead, only emerges in the semi-classical limit. Therefore, it is very natural to ask - what happens if we send a signal towards a corpuscular black hole? We show that quantum effects at the horizon scale imply the existence of a surface located at an effective radius $R=R_s(1+ε)$ slightly larger than the Schwarzschild radius $R_s,$ where $ε=1/N$ and $N$ is the number of gravitons composing the system. Consequently, the reflectivity of the object can be non-zero and, indeed, we find that incoming wave…
It is widely believed that exact global symmetries do not exist in theories that admit quantum black holes. Here we propose a way to quantify the degree of global symmetry violation in the Hawking radiation of a black hole by using certain relative entropies. While the violations of global symmetry that we consider are non-perturbative effects, they nevertheless give $\mathcal{O}(1)$ contributions to the relative entropy after the Page time. Furthermore, using "island" formulas, these relative entropies can be computed within semi-classical gravity, which we demonstrate with explicit examples.…
We consider four-dimensional dyonic single-center BPS black holes in the $N=2$ STU model of Sen and Vafa. By working in a region of moduli space where the real part of two of the three complex scalars $S, T, U$ are taken to be large, we evaluate the quantum entropy function for these BPS black holes. In this regime, the subleading corrections point to a microstate counting formula partly based on a Siegel modular form of weight two. This is supplemented by another modular object that takes into account the dependence on $Y^0$, a complex scalar field belonging to one of the four off-shell vecto…
Black hole photon spheres or light rings are closely linked to astronomical phenomena, such as the gravitational waves and the shadow in spherically symmetric or axi-symmetric spacetime. In Cunha and Herdeiro [Phys. Rev. Lett. 124, 181101 (2020)], a topological argument was applied for the four dimensional stationary, axi-symmetric, asymptotically flat black hole, and the result indicates that at least, there exists one standard light ring outside the black hole horizon for each rotation sense. Inspired by it, in this paper, we would like to consider a similar issue for a nonrotating, static, …
In this paper, we investigate the holographic complexity in the charged Taub-NUT-AdS black holes with Misner strings present in the Einstein-Maxwell gravity. We show that differing from the normal black holes, where the late-time complexity growth rate is only determined by the quantities at outer and inner ``Reissner-Nordstrom''-type (RN-type) horizons, here the quantities (the Misner potential and Misner charge) related to the Misner strings also play an important role in CA complexity. Similar to the case of the normal electromagnetic black hole, the late-time rate for the original CA conje…
We study traversable wormholes by considering the duality between BTZ black holes and two-dimensional conformal field theory on the thermofield double state. The BTZ black holes can be rendered traversable by a negative energy shock wave. Following Gao, Jafferis and Wall [1], we show that the negative energy shock wave is dual to the infinite boost limit of a specific double trace deformation which couples the left and right CFTs. We spell out the mechanism of information transfer through traversable BTZ wormholes, treating the backreaction of the message as a positive energy shockwave. The co…
