The instability of superfluids in optical lattice has been investigated using the holographic model. The static and steady flow solutions are numerically obtained from the static equations of motion and the solutions are described as Bloch waves with different Bloch wave vector $k$. Based on these Bloch waves, the instability is investigated at two levels. At the linear perturbation level, we show that there is a critical $k_{c}$ above which the superflow is unstable. At the fully nonlinear level, the intermediate state and final state of unstable superflow are identified through numerical simulation of the full equations of motion. The results show that during the time evolution, the unstable superflow will undergo a chaotic state, where solitons will appear and disappear. The system will settle down to a stable state with $k<k_{c}$ eventually, with a smaller current and a larger condensate.
We investigate the difference between holographic dark energy, Chaplygin gas, and tachyon model with constant potential. For this purpose, we examine their squared speeds of sound which are evaluated to zeroth order in perturbation theory and hence depends only on time. We find that the squared speed for holographic dark energy is always negative when choosing the future event horizon as the IR cutoff, while those for Chaplygin gas and tachyon are non-negative. This means that the perfect fluid for holographic dark energy is classically unstable. Hence the holographic interpretation for Chaply…
We present a calculation of two-point correlation functions of the stress-energy tensor in the strongly-coupled, confining gauge theory which is holographically dual to the AdS soliton geometry. The fact that the AdS soliton smoothly caps off at a certain point along the holographic direction, ensures that these correlators are dominated by quasinormal mode contributions and thus show an exponential decay in position space. In order to study such a field theory on a curved spacetime, we foliate the six-dimensional AdS soliton with a Schwarzschild black hole. Via gauge/gravity duality, this new…
The Anti-de Sitter (AdS) black hole with lattice structure plays an essential role in the study of the optical conductivity in holographic approach. We investigate the instability of this sort of black holes which may lead to the holographic description of charge density waves. In the presence of homogeneous axion fields, we show that the instability of AdS-Reissner-Nordström(AdS-RN) black hole is always suppressed. However, in the presence of Q-lattices, we find that the unstable region becomes the smallest in the vicinity of the critical region for metal/insulator phase transition. This nove…
We investigate the vacuum instability in the presence of dilaton field in a holographic set up. Although the dilaton is a bulk field, it leads to the vacuum instability on the boundary. We show that the whole process crucially depends on the probe brane position and as well on the radial coordinate. So that the effects of dilaton scale parameter in different regions of the bulk or for different probe brane positions are different. We also observe that in our study the temperature can strengthen the effect of scale parameter in reducing the potential barrier. Finally, we show that this Schwinge…
We report the observation of the spatially modulated static mode in the spectrum of fluctuations around the condensed phase of the holographic d-wave superconductor. The mode involves the time component of the gauge field that is related to the charge density wave in the dual superconductor. No additional ingredients are added to the action of five dimensional theory. We speculate on the relevance of the observed mode to the formation of the pseudogap state.
The holographic entanglement entropy of an infinite strip subsystem on the asymptotic AdS boundary is used as a probe to study the thermodynamic instabilities of planar R-charged black holes (or their dual field theories). We focus on the single-charge AdS black holes in $D=5$, which correspond to spinning D3-branes with one non-vanishing angular momentum. Our results show that the holographic entanglement entropy indeed exhibits the thermodynamic instability associated with the divergence of the specific heat. When the width of the strip is large enough, the finite part of the holographic ent…
In this paper we study the dynamical instability of Sakai-Sugimoto's holographic QCD model at finite baryon density. In this model, the baryon density, represented by the smeared instanton on the worldvolume of the probe D8-\overline{D8} mesonic brane, sources the worldvolume electric field, and through the Chern-Simons term it will induces the instability to form a chiral helical wave. This is similar to Deryagin-Grigoriev-Rubakov instability to form the chiral density wave for large N_c QCD at finite density. Our results show that this kind of instability occurs for sufficiently high baryon …
Using the AdS/CFT correspondence, we calculate the vacuum decay rate for the Schwinger effect in confining large $N_{c}$ gauge theories. The instability is induced by the quark antiquark pair creation triggered by strong electromagnetic fields. The decay rate is obtained as the imaginary part of the Euler-Heisenberg effective Lagrangian evaluated from the D-brane action with a constant electromagnetic field in holographic QCD models such as the Sakai-Sugimoto model and the deformed Sakai-Sugimoto model. The decay rate is found to increase with the magnetic field parallel to the electric field,…
We consider a holographic description of a system of strongly-coupled fermions in 2+1 dimensions based on a D7-brane probe in the background of D3-branes. The black hole embedding represents a Fermi-like liquid. We study the excitations of the Fermi liquid system. Above a critical density which depends on the temperature, the system becomes unstable towards an inhomogeneous modulated phase which is similar to a charge density and spin wave state. The essence of this instability can be effectively described by a Maxwell-axion theory with a background electric field. We also consider the fate of…
A smoking gun signature for a first-order phase transition with negative speed of sound squared $c_s^2$ is the occurrence of a spinodal instability. In the gauge/gravity duality it corresponds to a Gregory-Laflamme type instability, which can be numerically simulated as the evolution of unstable planar black branes. Making use of holography its dynamics is studied far from and near a critical point with the following results. Near a critical point the interface between cold and hot stable phases, given by its width and surface tension, is found to feature a wider phase separation and a smaller…
According to the gauge-gravity duality, we systematically study the Schwinger effect and electric instability with anisotropy in a top-down holographic approach. The anisotropic black brane and bubble (soliton) background in IIB supergravity are employed and the dual theories in these backgrounds are expected to be anisotropic theory at finite temperature and anisotropic theory with confinement respectively. Then performing the potential analysis, we find due to the anisotropy, the potential barrier behaves oppositely with parallel and perpendicular electric fields, and this behavior agrees wi…
The high energy thermodynamics of Little String Theory (LST) is known to be unstable. An unresolved question is whether the corresponding instability in LST holographic dual is of stringy or supergravity origin. We study UV thermodynamics of a large metric deformation of the LST dual realized (in the extremal case) by type IIB fivebranes wrapping a two-sphere of a resolved conifold, and demonstrate that the resulting black hole has negative specific heat. This explicitly shows that the high energy thermodynamic instability of the LST holographic dual is of the supergravity origin.
Gravitational falling in AdS has two characteristic properties \cite{ohsin}: i) A thick shell becomes a thin shell. ii) Any shape become spherical. Such focusing character of AdS, for the collapse of dusts, leads to the rapid thermalization mechanism in strongly interacting system. For the collapse of a wave, it explains the cascade of energy to UV through repeated bounces, which has been extensively discussed in recent numerical works. Therefore the focusing is the physical mechanism of instability of AdS. Such sharp contrast between the dust and wave in collapse, together with the experiment…
We review and extend previous results regarding the stability and thermodynamics of Anti-de Sitter (AdS) spacetime at finite temperature. Using a combination of analytic and numerical techniques, we compute the energy, temperature, and entropy of perfect fluid stars in asymptotically AdS spacetimes. We find that at sufficiently high temperature (in the canonical ensemble) or energy (in the microcanonical ensemble) these configurations develop dynamical instabilities, which presumably lead to the formation of a black hole. We extend our analysis to the case of $AdS \times S$ compactifications s…
In this study, we analyze the dynamical stability of the D3-D7 model dual to a holographic conductor with a constant current under an external electric field. We particularly focus on the stability around the parameter region where the multivalued relation between the external electric field and the current is shown due to nonlinear conductivity. The dynamical stability of the states can be analyzed by considering linear perturbations in the background states and computing the quasinormal modes. In the multivalued region, we find that the states in one branch with a low electric current can be…
We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS_4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly m…
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 study three properties of a holographic superconductor related to conductivities, where momentum relaxation plays an important role. First, we find that there are constraints between electric, thermoelectric and thermal conductivities. The constraints are analytically derived by the Ward identities regarding diffeomorphism from field theory perspective. We confirm them by numerically computing all two-point functions from holographic perspective. Second, we investigate Homes' law and Uemura's law for various high-temperature and conventional superconductors. They are empirical and (material…
We use gauge/gravity duality to investigate the effect of thermal fluctuations on the dissociation of the quarkonium meson in strongly coupled $(3+1)$-dimensional gauge theories. This is done by studying the instability and probable first order phase transition of a probe D7-brane in the dual gravity theory. We explicitly show that for the Minkowski embeddings with their tips close to the horizon in the background, the long wavelength thermal fluctuations lead to an imaginary term in their action signaling an instability in the system. Due to this instability, a phase transition is expected. O…
In holographic applications one can encounter scenarios where a long-wavelength instability can arise. In such situations, it is often the case that the dynamical end point of the instability is a new equilibrium phase with a nonlinear scalar hair condensate outside the black hole horizon. We here review holographic setups where symmetric horizons suffer from long-wavelength instabilities where a suitable equilibrium condensate phase does not exist. We study the dynamics of the simplest model in this exotic class, and show that it uncovers arbitrarily large curvatures in the vicinity of the ho…
We study the instability, for the supersymmetric Yang-Mills (SYM) theories, caused by the external electric field through the imaginary part of the action of the D7 probe brane, which is embedded in the background of type IIB theory. This instability is related to the Schwinger effect, namely to the quark pair production due to the external electric field, for the $SU(N_c)$ SYM theories. In this holographic approach, it is possible to calculate the Schwinger effect for various phases of the theories. Here we give the calculation for ${\cal N}=2$ SYM theory and the analysis is extended to the f…
In a holographic probe-brane model exhibiting a spontaneously spatially modulated ground state, we introduce explicit sources of symmetry breaking in the form of ionic and antiferromagnetic lattices. For the first time in a holographic model, we demonstrate pinning, in which the translational Goldstone mode is lifted by the introduction of explicit sources of translational symmetry breaking. The numerically computed optical conductivity fits very well to a Drude-Lorentz model with a small residual metallicity, precisely matching analytic formulas for the DC conductivity. We also find an instab…
We perform a perturbative (near-critical) analysis of the stability of an asymptotically Schroedinger Reissner-Nordstrom black hole with respect to generation of charged scalar hair. We find that apart from the expected instability at low temperatures typical of holographic models of superconductivity, in the presence of certain operators a similar instability appears as well at high temperatures. We propose that the reason for such a phase diagram could be due to peculiar features of the dual gauge theory or the failure of the model to provide a consistent holographic dual of a non-relativist…
We study a simple extension of the original Hartnoll, Herzog and Horowitz (HHH) holographic superfluid model with two nonlinear scalar self-interaction terms $λ|ψ|^4$ and $τ|ψ|^6$ in the probe limit. Depending on the value of $λ$ and $τ$, this setup allows us to realize a large spectrum of holographic phase transitions which are 2nd, 1st and 0th order as well as the ``cave of wind'' phase transition. We speculate the landscape pictures and explore the near equilibrium dynamics of the lowest quasinormal modes (QNMs) across the whole phase diagram at both zero and finite wave-vector. We find tha…
We explore the end point of the helical instability in finite density, finite magnetic field background discussed by Kharzeev and Yee [1]. The nonlinear solution is obtained and identified with the (magnetized) chiral density wave phase in literature. We find there are two branches of solutions, which match with the two unstable modes in [1]. At large chemical potential and magnetic field, the magnetized chiral density wave can be thermodynamically preferred over chirally symmetric phase and chiral symmetry breaking phase. Interestingly, we find an exotic state with vanishing chemical potentia…
We study the spectral function of fermions in a holographic set up with bulk Dirac mass in the regime beyond the conformal unitarity bound, and find that spectral function has the dispersion relation with tachyonic behavior, indicating an instability. Based on linearity between the density and the position of the tip of the k-gap, we suggest that this instability is toward the charge density wave(CDW) and the position of the tip can be identified as the wave vector of CDW. For the physical origin, we point out the similarity of unitarity violation in our non-Fermi Liquid theory and nesting phe…
An interesting application of the gauge/gravity duality to condensed matter physics is the description of a lattice via breaking translational invariance on the gravity side. By making use of global symmetries, it is possible to do so without scarifying homogeneity of the pertinent bulk solutions, which we thus term as "homogeneous holographic lattices." Due to their technical simplicity, these configurations have received a great deal of attention in the last few years and have been shown to correctly describe momentum relaxation and hence (finite) DC conductivities. However, it is not clear …
In the probe limit, we study the holographic $p$-wave phase transition in the Gauss-Bonnet gravity via numerical and analytical methods. Concretely, we study the influences of the external magnetic field on the Maxwell complex vector model in the five-dimensional Gauss-Bonnet-AdS black hole and soliton backgrounds, respectively. For the two backgrounds, the results show that the magnetic field enhances the superconductor phase transition in the case of the lowest Landau level, while the increasing Gauss-Bonnet parameter always hinders the vector condensate. Moreover, the Maxwell complex vector…
Lattice Monte Carlo studies in SU(3) gauge theory have shown that the topological charge distribution in the vacuum is dominated by thin coherent membranes of codimension one arranged in a layered, alternating-sign sandwich. A similar lamination of topological charge occurs in the 2D $CP^{N-1}$ model. In holographic QCD, the observed topological charge sheets are naturally interpreted as $D6$ branes wrapped around an $S_4$.. With this interpretation, the laminated array of topological charge membranes observed on the lattice can be identified as a "tachyonic crystal", a regular, alternating-si…
