Four-dimensional $\mathcal{N}=4$ supersymmetric Yang-Mills theory, at a point on the Coulomb branch where $SU(N)$ gauge symmetry is spontaneously broken to $SU(N-1)\times U(1)$, admits BPS solitons describing a spherical shell of electric and/or magnetic charges enclosing a region of unbroken gauge symmetry. These solitons have been proposed as gauge theory models for certain features of asymptotically flat extremal black holes. In the 't Hooft large $N$ limit with large 't Hooft coupling, these solitons are holographically dual to certain probe D3-branes in the $AdS_5 \times S^5$ solution of type IIB supergravity. By studying linearised perturbations of these D3-branes, we show that the solitons support quasinormal modes with a spectrum of frequencies sharing both qualitative and quantitative features with asymptotically flat extremal black holes.
In this work we aim at discussing the effects of higher order corrections to curvature on the Lovelock AdS black holes quasinormal spectrum and, in the context of gauge/gravity correspondence, their consequences for the formation of holographic superconductors. We also explore the hydrodynamic limit of the $U(1)$ gauge field perturbations in $d$ dimensions.
We show that in field theories with a holographic dual the retarded Green's function of a conserved current can be represented as a convergent sum over the quasinormal modes. We find that the zero-frequency conductivity is related to the sum over quasinormal modes and their high-frequency asymptotics via a sum rule. We derive the asymptotics of the quasinormal mode frequencies and their residues using the phase-integral (WKB) approach and provide analytic insight into the existing numerical observations concerning the asymptotic behavior of the spectral densities.
Here we shall show that there is no other instability for the Einstein-Gauss-Bonnet-anti-de Sitter (AdS) black holes, than the eikonal one and consider the features of the quasinormal spectrum in the stability sector in detail. The obtained quasinormal spectrum consists from the two essentially different types of modes: perturbative and non-perturbative in the Gauss-Bonnet coupling $α$. The sound and hydrodynamic modes of the perturbative branch can be expressed through their Schwazrschild-AdS limits by adding a linear in $α$ correction to the damping rates: $ω\approx Re(ω_{SAdS}) - Im(ω_{SAdS…
We provide a framework for calculating holographic Green's functions from general bilinear actions and fields obeying coupled differential equations in the bulk. The matrix-valued spectral function is shown to be independent of the radial bulk coordinate. Applying this framework we improve the analysis of fluctuations in the D3/D7 system at finite baryon density, where the longitudinal perturbations of the world-volume gauge field couple to the scalar fluctuations of the brane embedding. We compute the spectral function and show how its properties are related to the quasinormal mode spectrum. …
Black holes in anti-de Sitter (AdS) backgrounds play a pivotal role in the gauge/gravity duality where they determine, among other things, the approach to equilibrium of the dual field theory. We undertake a detailed analysis of perturbed Kerr-AdS black holes in four- and five-dimensional spacetimes, including the computation of its quasinormal modes, hydrodynamic modes and superradiantly unstable modes. Our results shed light on the possibility of new black hole phases with a single Killing field, possible new holographic phenomena and phases in the presence of a rotating chemical potential, …
We study the holographic duals of bosonic and fermionic fields and compute their Quasinormal Frequencies (QNF) by exploiting that they are massive charged fields in $\mathrm{AdS_2 \times \mathcal{K}}$. In particular, we assess the stability of the scalar and fermionic operators in Myers-Perry's black holes with equal angular momenta. We compute the central charge and the Hawking-entropy and introduce extremality parameters to determine the properties of the dual CFT. Then, we briefly discuss how detection of Spin-2 fields can pave the way for more deep understanding of the holographic principl…
We study the propagation of probe scalar fields in the background of 4D Einstein-Gauss-Bonnet black holes with anti-de Sitter (AdS) asymptotics and calculate the quasinormal modes. Mainly, we show that the quasinormal spectrum consists of two different branches, a branch perturbative in the Gauss-Bonnet coupling constant $α$ and another branch nonperturbative in $α$. The perturbative branch consists of complex quasinormal frequencies that approximate to the quasinormal frequencies of the Schwarzschild AdS black hole in the limit of a null coupling constant. On the other hand, the nonperturbati…
We study the quasinormal modes and non-linear dynamics of a simplified model of semi-holography, which consistently integrates mutually interacting perturbative and strongly coupled holographic degrees of freedom such that the full system has a total conserved energy. We show that the thermalization of the full system can be parametrically slow when the mutual coupling is weak. For typical homogeneous initial states, we find that initially energy is transferred from the black brane to the perturbative sector, later giving way to complete transfer of energy to the black brane at a slow and cons…
Gauss-Bonnet holographic fluid is a useful theoretical laboratory to study the effects of curvature-squared terms in the dual gravity action on transport coefficients, quasinormal spectra and the analytic structure of thermal correlators at strong coupling. To understand the behavior and possible pathologies of the Gauss-Bonnet fluid in $3+1$ dimensions, we compute (analytically and non-perturbatively in the Gauss-Bonnet coupling) its second-order transport coefficients, the retarded two- and three-point correlation functions of the energy-momentum tensor in the hydrodynamic regime as well as …
Following a series of similar calculations in simpler non-conformal holographic setups, we determine the quasinormal mode spectrum for an operator dual to a gauge-invariant scalar field within the Improved Holographic QCD framework. At temperatures somewhat above the critical temperature of the deconfinement transition, we find a small number of clearly separated modes followed by a branch-cut-like structure parallel to the real axis, the presence of which is linked to the form of the IHQCD potential employed. The temperature dependence of the lowest nonzero mode is furthermore used to study t…
A holographic model for QCD is employed to investigate the effects of the gluon condensate on the spectrum and melting of scalar mesons. We find the evolution of the free energy density with the temperature, and the result shows that the temperature of the confinement/deconfinement transition is sensitive to the gluon-condensate parameter. The spectral functions (SPFs) are also obtained and show a series of peaks in the low-temperature regime, indicating the presence of quasiparticle states associated to the mesons, while the number of peaks decreases with the increment of the temperature, cha…
We calculate frequency space holographic correlators in an asymptotically AdS crunching background, dual to a relevant deformation of the M2-brane CFT placed in de Sitter spacetime. For massless bulk scalars, exploiting the connection to a solvable supersymmetric quantum mechanical problem, we obtain the exact frequency space correlator for the dual operator in the deformed CFT. Controlling the shape of the crunching surface in the Penrose diagram by smoothly dialling the deformation from zero to infinity, we observe that in the large deformation limit the Penrose diagram becomes a `square', a…
Perturbations of asymptotically Anti-de-Sitter (AdS) spacetimes are often considered by imposing field vanishing boundary conditions (BCs) at the AdS boundary. Such BCs, of Dirichlet-type, imply a vanishing energy flux at the boundary, but the converse is, generically, not true. Regarding AdS as a gravitational box, we consider vanishing energy flux (VEF) BCs as a more fundamental physical requirement and we show that these BCs can lead to a new branch of modes. As a concrete example, we consider Maxwell perturbations on Kerr-AdS black holes in the Teukolsky formalism, but our formulation appl…
We show that nearly extremal Kerr black holes have two distinct sets of quasinormal modes, which we call zero-damping modes (ZDMs) and damped modes (DMs). The ZDMs exist for all harmonic indices $l$ and $m \ge 0$, and their frequencies cluster onto the real axis in the extremal limit. The DMs have nonzero damping for all black hole spins; they exist for all counterrotating modes ($m<0$) and for corotating modes with $0\leq μ\lesssim μ_c=0.74$ (in the eikonal limit), where $μ\equiv m/(l+1/2)$. When the two families coexist, ZDMs and DMs merge to form a single set of quasinormal modes as the bla…
The AdS/CFT correspondence has developed over the last years into a very useful and powerful tool for studying strongly coupled field theories at finite temperature and density. Of particular interest is the regime of near equilibrium real time evolution that can be captured via linear response theory. The AdS/CFT correspondence allows the calculation of retarded two point functions of gauge invariant operators by studying fluctuations around asymptotically AdS black holes. A major role is played by the poles of these holographic response functions: the quasinormal frequencies. I will review t…
In a study of the quasinormal mode frequencies of nearly extremal black holes, we pointed out a bifurcation of the mode spectrum into modes with finite decay and modes with vanishing decay in the extremal limit. We provided analytic and semi-analytic results identifying which families of modes bifurcated, and when modes with finite decay rates exist when approaching the extremal limit. In a recent note (arXiv:1510.05604), Hod suggests that additional modes asymptote to finite decay at extremely high spin parameter, based on past work by Detweiler. We search for these suggested modes and find n…
We study fluctuations of a U(1) gauge field on the worldvolume of Nf probe D7-branes in the background of Nc black D3-branes with a finite baryon density. The choice of mode corresponds to vector mesons in the dual gauge theory whose mass and lifetime can be determined by a study of the quasinormal modes. The speed of propagation of these holographic mesons at large momenta is studied from the dispersion relations of the quasinormal modes of the system.
We show that the quasinormal spectrum of gravitational perturbations of Schwarzschild - de Sitter black holes contains a new branch of purely imaginary modes. These modes are not algebraically special and we showed that the sum of them form the well-known in the literature exponential asymptotic tail. When the ratio of the event horizon radius to the cosmological horizon vanishes, these quasinormal modes approach modes of empty de Sitter spacetime. Thus, the spectrum consists of the two branches: Schwarzschild branch deformed by the cosmological constant and de Sitter branch deformed by the bl…
We study the poles of the retarded Green functions of a holographic superconductor. The model shows a second order phase transition where a charged scalar operator condenses and a U(1) symmetry is spontaneously broken. The poles of the holographic Green functions are the quasinormal modes in an AdS black hole background. We study the spectrum of quasinormal frequencies in the broken phase, where we establish the appearance of a massless or hydrodynamic mode at the critical temperature as expected for a second order phase transition. In the broken phase we find the pole representing second soun…
In this work, we present the quasinormal modes of a fermionic field in the background of Gauss-Bonnet-AdS black holes. We find exact solutions for $D=5$ at the fixed value $α=R^2/2$ of the Gauss--Bonnet coupling constant, with $R$ denoting the AdS radius, and we find numerical solutions for some range of values of the coupling constant $α$ and $D=5, 6$. Mainly, we find two branches of quasinormal frequencies, a branch perturbative in the Gauss-Bonnet coupling constant $α$, and another branch nonperturbative in $α$. The phenomena of nonperturbative modes, which seem to be quite general in theor…
We derive an expression for functional determinants in thermal spacetimes as a product over the corresponding quasinormal modes. As simple applications we give efficient computations of scalar determinants in thermal AdS, BTZ black hole and de Sitter spacetimes. We emphasize the conceptual utility of our formula for discussing `1/N' corrections to strongly coupled field theories via the holographic correspondence.
The motion of a small compact object in a curved background spacetime deviates from a geodesic due to the action of its own field, giving rise to a self-force. This self-force may be calculated by integrating the Green function for the wave equation over the past worldline of the small object. We compute the self-force in this way for the case of a scalar charge in Schwarzschild spacetime, making use of the semi-analytic method of matched Green function expansions. Inside a local neighbourhood of the compact object, this method uses the Hadamard form for the Green function in order to render r…
It has recently been found that quasinormal modes of asymptotically anti-de Sitter (AdS) black holes in theories with higher curvature corrections may help to describe the regime of intermediate 't Hooft coupling in the dual field theory. Here, we consider quasinormal modes of a scalar field in the background of spherical Gauss--Bonnet--anti-de Sitter (AdS) black holes. In general, the eigenvalues of wave equations are found here numerically, but at a fixed Gauss-Bonnet constant $α= R^2/2$ (where $R$ is the AdS radius), an exact solution of the scalar field equation has been obtained. Remarkab…
Quasinormal frequencies of electromagnetic and gravitational perturbations in asymptotically AdS spacetime can be identified with poles of the corresponding real-time Green's functions in a holographically dual finite temperature field theory. The quasinormal modes are defined for gauge-invariant quantities which obey incoming-wave boundary condition at the horizon and Dirichlet condition at the boundary. As an application, we explicitly find poles of retarded correlation functions of R-symmetry currents and the energy-momentum tensor in strongly coupled finite temperature N=4 supersymmetric S…
We compute the quasinormal modes (QNMs) of a massive scalar field in the background of a rotating three-dimensional Hořava AdS black hole, and we analyze the effect of the breaking of the Lorentz invariance on the QNMs. Imposing on the horizon that there are only ingoing waves and at infinity the Dirichlet boundary conditions and the Neumann boundary condition, we calculate the oscillatory and the decay modes of the QNMs. We find that the propagation of the scalar field is stable in this background and employing the holographic principle we find the different times of the perturbed system to r…
Null geodesics, quasinormal modes of a massless scalar field perturbation and the correspondence with shadow radii are investigated in the background spacetime of high-dimensional Einstein-Yang-Mills black holes. Based on the properties of null geodesics, we obtain the connection between the radius of a photon sphere and the radius of a horizon in the five- and six-dimensional Einstein-Yang-Mills spacetimes. Especially in the five-dimensional case, there exist two branches for the radius of a photon sphere, but only the branch outside the event horizon satisfies the condition of circular null …
We revisit the holographic calculation of the decay modes of the BTZ blackhole perturbed by a scalar probe. We carry out a finite temperature expansion of the torus two point function of large central charge $(c)$ CFTs in order to obtain the corrections to blackhole quasinormal modes. We take the contribution of the lightest primary above the vacuum, with dimension $Δ_χ$ and upper bound of $c/6$, in the torus two point function. We exploit the modular properties of 2D CFT on the torus to connect the expression of thermal two point function at high temperature with the same at low temperature. …
We study dynamical condensation process in a holographic superconductor model with anisotropy. The time-dependent numerical solution is constructed for the Einstein-Maxwell-dilaton theory with complex scalar in asymptotic AdS spacetime. The introduction of dilaton field generates the anisotropy in boundary spatial directions. In analogy of isotropic case, we have two black hole solutions below certain critical temperature $T_c$, the anisotropic charged black hole with and without scalar hair, corresponding respectively to the supercooled normal phase and superconducting phase in the boundary t…
We compute the homogeneous limit of non-hydrodynamic quasinormal modes (QNM's) of a phenomenologically realistic Einstein-Maxwell-Dilaton (EMD) holographic model for the Quark-Gluon Plasma (QGP) that is able to: i) {\it quantitatively} describe state-of-the-art lattice results for the QCD equation of state and higher order baryon susceptibilities with $2+1$ flavors and physical quark masses up to highest values of the baryon chemical potential currently reached in lattice simulations; ii) describe the nearly perfect fluidity of the strongly coupled QGP produced in ultrarelativistic heavy ion c…
Branch-dependent ringdown in black-bounce spacetimes: imprints of matter-source ambiguity on quasinormal modes
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院，中国科学院大学）；Department of Physics, Yantai University（烟台大学物理学院）
Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex-frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for arbitrary values of the frequency. The branch cut yields a power-law tail decay for late times in the response of a black hole to an initial perturbation. We determine explicitly the first three orders in…
We perform the stability analysis on scalarized charged black holes in the Einstein-Maxwell-Scalar (EMS) theory by computing quasinormal mode spectrum. It is noted that the appearance of these black holes with scalar hair is closely related to the instability of Reissner-Nordström black holes without scalar hair in the EMS theory. The scalarized black hole solutions are classified by the node number of $n=0,1,2,\cdots$, where $n=0$ is called the fundamental branch and $n=1,2,\cdots$ denote the $n$ excited branches. Here, we show that the $n=1,2$ excited black holes are unstable against against…
We revisit the question of stability of holographic superfluids with finite superfluid velocity. Our method is based on applying the Landau criterion to the Quasinormal Mode (QNM) spectrum. In particular we study the QNMs related to the Goldstone modes of spontaneous symmetry breaking with linear and quadratic dispersions.In the linear case we show that the sound velocity becomes negative for large enough superfluid velocity and that the imaginary part of the quasinormal frequency moves to the upper half plane. Since the instability is strongest at finite wavelength, we take this as an indicat…
We study the spectrum of vector mesons in a finite temperature plasma. The plasma is holographically described by a black hole AdS/QCD model. We compute the boundary retarded Green's function using AdS/CFT prescriptions. The corresponding thermal spectral functions show quasiparticle peaks at low temperatures. Then we calculate the quasinormal modes of vector mesons in the soft-wall black hole geometry and analyse their temperature and momentum dependences.
Finite 't Hooft coupling corrections to multiple physical observables in strongly coupled $N=4$ supersymmetric Yang-Mills plasma are examined, in an attempt to assess the stability of the expansion in inverse powers of the 't Hooft coupling $λ$. Observables considered include thermodynamic quantities, transport coefficients, and quasinormal mode frequencies. Although large $λ$ expansions for quasinormal mode frequencies are notably less well behaved than the expansions of other quantities, we find that a partial resummation of higher order corrections can significantly reduce the sensitivity o…
We compute the gravitational quasinormal modes of the global AdS_5-Schwarzschild solution. We show how to use the holographic dual of these modes to describe a thermal plasma of finite extent expanding in a slightly anisotropic fashion. We compare these flows with the behavior of quark-gluon plasmas produced in relativistic heavy ion collisions by estimating the elliptic flow coefficient and the thermalization time.
We study the scalar and vector channels of gravitational quasinormal modes for Lifshitz black branes emerging in Einstein-Maxwell-Dilaton and Einstein-Proca theories in four and five dimensions, finding significant differences between the two models. In particular, rather surprisingly, in the Einstein-Maxwell-Dilaton model the dispersion relations for the shear and sound modes are given by $ω_{shear} \sim -i\,k^4$ and $ω_{sound}\sim-i \,k^2$, while in the Einstein-Proca model they take the more conventional form $ω_{shear} \sim -i\,k^2$ and $ω_{sound}\sim k$, the proportionality constants depe…
We examine the mesonic thermal spectrum of the Sakai-Sugimoto model of holographic QCD by finding the quasinormal frequencies of the supergravity dual. If flavour is added using D8 and anti-D8 branes there exist embeddings where the D-brane worldvolume contains a black hole. For these embeddings (the high-temperature phase of the Sakai-Sugimoto model) we determine the quasinormal spectra of scalar and vector mesons arising from the worldvolume DBI action of the D-brane. We stress the importance of a coordinate change that makes the in-falling quasinormal modes regular at the horizon allowing a…
We study non-equilibrium dynamics and quantum quenches in a recent gauge/gravity duality model for a strongly coupled system interacting with a magnetic impurity with $SU(N)$ spin. At large $N$, it is convenient to write the impurity spin as a bilinear in Abrikosov fermions. The model describes an RG flow triggered by the marginally relevant Kondo operator. There is a phase transition at a critical temperature, below which an operator condenses which involves both an electron and an Abrikosov fermion field. This corresponds to a holographic superconductor in AdS$_2$ and models the impurity scr…
We point out an elementary thermodynamics fact that whenever the specific heat of a system is negative, the speed of sound in such a media is imaginary. The latter observation presents a proof of Gubser-Mitra conjecture on the relation between dynamical and thermodynamic instabilities for gravitational backgrounds with a translationary invariant horizon, provided such geometries can be interpreted as holographic duals to finite temperature gauge theories. It further identifies a tachyonic mode of the Gubser-Mitra instability (the lowest quasinormal mode of the corresponding horizon geometry) a…
We obtain relaxation times for field theories with Lifshitz scaling and with holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by computing quasinormal modes of a bulk scalar field in the presence of Lifshitz black branes. We determine the relation between relaxation time and dynamical exponent z, for various values of boundary dimension d and operator scaling dimension. It is found that for d>z+1, at zero momenta, the modes are non-overdamped, whereas for d<=z+1 the system is always overdamped. For d=z+1 and zero momenta, we present analytical results.
We develop a method to study coupled dynamics of gauge-invariant variables, constructed out of metric and gauge field fluctuations on the background of a AdS$_5$ Reissner-Nordström black brane. Using this method, we compute the numerical spectrum of quasinormal modes associated with fluctuations of spin 0, 1 and 2, non-perturbatively in $μ/T$. We also analytically compute the spectrum of hydrodynamic excitations in the small chemical potential limit. Then, by studying the spectral curve at complex momenta in every spin channel, we numerically find points at which hydrodynamic and non-hydrodyna…
We show that there exists a precise kinematical notion of holography for the Euclidean warped $AdS_3$ black hole. This follows from the fact that the Euclidean warped $AdS_3$ black hole spacetime is a geometrically finite hyperbolic manifold. For such manifolds a theorem of Sullivan provides a one-to-one correspondence between the hyperbolic structure in the bulk and the conformal structure of its boundary. Using this theorem we obtain the holographic quasinormal modes for the warped $AdS_3$ black hole.
The electromagnetic and gravitational quasinormal spectra of $(3+1)$-dimensional plane-symmetric anti-de Sitter black holes are analyzed in the context of the AdS/CFT correspondence. According to such a correspondence, the electromagnetic and gravitational quasinormal frequencies of these black holes are associated respectively to the poles of retarded correlation functions of $R$-symmetry currents and stress-energy tensor in the holographically dual conformal field theory: the $(2+1)$-dimensional $\mathcal{N}=8$ super-Yang-Mills theory. The connection between AdS black holes and the correspon…
We investigate the effect of external magnetic fields on equilibration in the improved holographic QCD theory in the deconfined phase using the AdS/CFT correspondence. In particular we calculate the quasinormal mode spectra in the corresponding black brane solutions and study their dependence on temperature, momentum and magnetic field, both in the scalar and the shear channels. We find complex patterns in the motion of quasinormal modes on the complex plane, including certain cross overs between the lowest lying modes under varying magnetic field, momentum and temperature. We also discover a …
We study the dynamics of a 2+1 dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the "gravity/fluid correspondence", to 3+1 dimensional asymptotically anti-de Sitter (AAdS) black brane solutions to the Einstein equation. We examine stability properties of shear flows, which correspond to hydrodynamic quasinormal modes of the black brane. We find that, for sufficiently high Reynolds number, the solution undergoes an inverse turbulent cascade to long wavelength modes. We then map this fluid solution, via the gravity/fluid duality,…
We study the quasinormal modes and thermal radiation of massless spin-0 field perturbations in the background of four-dimensional (4D) non-Abelian charged Lifshitz black branes with $z=2$ hyperscaling violation, which correspond to systems with superconducting fluctuations. After having an analytical solution to the Klein-Gordon equation, we obtain exact quasinormal modes that are purely imaginary. Therefore, there is no oscillatory behavior in the perturbations that guarantees the mode stability of these solutions. We also study the greybody factors, absorption cross-section, and decay rate o…
We provide an in-depth investigation of quasinormal-mode oscillations of Kerr black holes with nearly extremal angular momenta. We first discuss in greater detail the two distinct types of quasinormal mode frequencies presented in a recent paper (arXiv:1212.3271). One set of modes, that we call "zero-damping modes", has vanishing imaginary part in the extremal limit, and exists for all corotating perturbations (i.e., modes with azimuthal index m being nonnegative). The other set (the "damped modes") retains a finite decay rate even for extremal Kerr black holes, and exists only for a subset of…
Heavy vector mesons detected after a heavy ion collision are important sources of information about the quark gluon plasma. The fraction of such particles that survive the plasma phase and reach the detectors is related to the dissociation degree inside the thermal medium. A consistent picture for the thermal behavior of charmonium and bottomonium quasi-states in a thermal medium was obtained recently using a holographic bottom up model. This model captures the heavy flavour spectroscopy of masses and decay constants in the vacuum (zero temperature) and is consistently extended to finite tempe…
In this work we study the relaxation of the system of strongly correlated electrons, at charge neutrality, when the chemical potential undergoes a local change. This setup is a model for for the X-ray absorbtion edge study in the half-filled graphene. We use holographic duality to describe the system as a classical Schwarzschild black hole in curved 4-dimensional AdS spacetime. Assuming the amplitude of the quench is small, we neglect the backreaction on the geometry. We numerically study the two relaxation regimes: the adiabatic relaxation when the quench is slow and the relaxation governed b…
