AdS Soliton Background Research Articles

Holographic insulator/superconductor phase transitions with excited states

We construct a family of solutions of the holographic insulator/superconductor phase transitions with the excited states in the AdS soliton background by using both the numerical and analytical methods. The interesting point is that the improved Sturm-Liouville method can not only analytically investigate the properties of the phase transition with the excited states, but also the distributions of the condensed fields in the vicinity of the critical point. We observe that, regardless of the type of the holographic model, the excited state has a higher critical chemical potential than the corresponding ground state, and the difference of the dimensionless critical chemical potential between the consecutive states is around 2.4, which is different from the finding of the metal/superconductor phase transition in the AdS black hole background. Furthermore, near the critical point, we find that the phase transition of the systems is of the second order and a linear relationship exists between the charge density and chemical potential for all the excited states in both s-wave and p-wave insulator/superconductor models.

Analytical study of holographic p-wave superfluid models in Gauss\u2013Bonnet gravity

In Gauss–Bonnet gravity, we analytically investigate the p-wave superfluid models in five dimensional AdS soliton and AdS black hole in order to explore the influences of the higher curvature correction on the holographic superfluid phase transition. We observe that the analytical findings are in good agreement with the numerical computations. Our results show that the critical chemical potential of the system increases with the increase of the Gauss–Bonnet parameter in AdS soliton background, while the critical temperature decreases as the Gauss–Bonnet factor grows if the phase transition of the system is of the second order in AdS black hole background, both of which indicate that the higher curvature correction hinders the formation of the condensation of the vector operator. Moreover, the critical exponent of the system takes the mean-field value 1/2, which is independent of the Gauss–Bonnet parameter and the spatial component of the gauge field.

Holographic p-wave superfluid in the AdS soliton background with RF2 corrections

We investigate the holographic p-wave superfluid in the background metric of the AdS soliton with RF2 corrections. Two models, namely, the Maxwell complex vector field model and Yang-Mills theory, are studied in the above context by employing the Sturm-Liouville approach as well as the shooting method. When turning on the spatial components of the gauge field, one observes that, in the probe limit, the inclusion of RF2 corrections hinders the superfluid phase transition. On the other hand, however, in the absence of the superfluid velocity, it is found that the RF2 corrections lead to distinct effects for the two models. Regardless of either the RF2 correction or the spatial component of the gauge field, the phase transition of the system is observed to be always of the second order. Moreover, a linear relationship between the charge density and chemical potential is largely established near the critical point in both holographic superfluid models.

Complexity growth rate during phase transitions

We present evidences for the connection between the potential of different fields and complexity growth rates both in conformal and confining cases. By studying different models, we also establish a strong connection between phase transitions and the discontinuities in the complexity growth rates. In the first example, for the dyonic black holes which are dual to van der Waals fluids, we find a similar first order phase transition in the behavior of complexity growth rate. We then compare the Schwinger effect and also the behavior of complexity in the AdS and AdS soliton backgrounds and comment on the connection between them. Finally, in a general Gubser model of QCD, we present the connections between the potentials, entropies, speed of sounds and complexity growth rates during crossover, first and second order phase transitions and also the behavior of quasinormal modes.

Analytical studies on holographic superconductor in the probe limit

We investigate the holographic superconductor model constructed in the (2[Formula: see text]+[Formula: see text]1)-dimensional AdS soliton background in the probe limit. With analytical methods, we obtain the formula of critical phase transition points with respect to the scalar mass. We also generalize this formula to higher-dimensional space–time. We mention that these formulas are precise compared to numerical results. In addition, we find a correspondence between the value of the charged scalar field at the tip and the scalar operator at infinity around the phase transition points.

A general holographic insulator/superconductor model with dark matter sector away from the probe limit

We investigate holographic phase transitions with dark matter sector in the AdS soliton background away from the probe limit. In cases of weak backreaction, we find that the larger coupling parameter α makes the gap of condensation shallower and the critical chemical potential keeps as a constant. In contrast, for very heavy backreaction, the dark matter sector could affect the critical chemical potential and the order of phase transitions. We also find the jump of the holographic topological entanglement entropy corresponds to a first order transition between superconducting states in this model with dark matter sector. More importantly, for certain sets of parameters, we observe novel phenomenon of retrograde condensation. In a word, the dark matter sector provides richer physics in the phase structure and the holographic superconductor properties are helpful in understanding dark matter.

Holographic Chern-Simons defects

We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7-branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for two-dimensional QCD.

Observing the inhomogeneity in the holographic models of superconductors

We study the gravity duals of striped holographic superconductors in the AdS black hole and AdS soliton backgrounds. We show the dependences of the condensation and the critical temperature/critical chemical potential on the inhomogeneity in these two different spacetimes. By exploring the dynamics of the normal phase through the scalar field perturbation, we argue that the pair susceptibility and the conductivity can be possible phenomenological indications to disclose the property of inhomogeneity.

Vector condensate and AdS soliton instability induced by a magnetic field

We continue to study the holographic p-wave superconductor model in the Einstein-Maxwell-complex vector field theory with a non-minimal coupling between the complex vector field and the Maxwell field. In this paper we work in the AdS soliton background which describes a conformal field theory in the confined phase and focus on the probe approximation. We find that an applied magnetic field can lead to the condensate of the vector field and the AdS soliton instability. As a result, a vortex lattice structure forms in the spatial directions perpendicular to the applied magnetic field. As a comparison, we also discuss the vector condensate in the Einstein-SU(2) Yang-Mills theory and find that in the setup of the present paper, the Einstein-Maxwell-complex vector field model is a generalization of the SU(2) model in the sense that the vector field has a general mass and gyromagnetic ratio.

Holographic collisions in confining theories

We study the gravitational dual of a high-energy collision in a confining gauge theory. We consider a linearized approach in which two point particles traveling in an AdS-soliton background suddenly collide to form an object at rest (presumably a black hole for large enough center-of-mass energies). The resulting radiation exhibits the features expected in a theory with a mass gap: late-time power law tails of the form t^(-3/2), the failure of Huygens' principle and distortion of the wave pattern as it propagates. The energy spectrum is exponentially suppressed for frequencies smaller than the gauge theory mass gap. Consequently, we observe no memory effect in the gravitational waveforms. At larger frequencies the spectrum has an upward-stairway structure, which corresponds to the excitation of the tower of massive states in the confining gauge theory. We discuss the importance of phenomenological cutoffs to regularize the divergent spectrum, and the aspects of the full non-linear collision that are expected to be captured by our approach.

Confining backgrounds and quantum chaos in holography

Classical world-sheet string theory has recently been shown to be nonintegrable and chaotic in various confining string theory backgrounds – the AdS soliton background in particular. In this Letter we study a minisuperspace quantization of the theory and look at properties of the spectrum like the distribution of level spacing, which are indicative of quantum order or chaos. In the quantum spectrum we find a gradual transition from chaotic (Wigner GOE) to integrable (Poisson) regime as we look at higher energies. This is expected since our system is integrable asymptotically, and at higher energies, the dynamics is entirely dominated by the kinetic terms.

Striped phases in the holographic insulator/superconductor transition

We study striped phases in holographic insulator/superconductor transition by considering a spatially modulated chemical potential in AdS soliton background. Generally striped phases can develop above a critical chemical potential. When the constant leading term in the chemical potential is set to zero, a discontinuity in the plot of charge density versus chemical potential is observed in the limit of large wave vector. We explain this discontinuity using an analytical approach. When the constant leading term in the chemical potential is present, the critical chemical potential is larger than in the case of a homogeneous chemical potential, which indicates that the spatially modulated chemical potential disfavors the phase transition. This behavior is also confirmed qualitatively by analytical calculations. We also calculate the grand canonical potential and find that the striped phase is favored.

Holographic droplets in p-wave insulator/superconductor transition

In the present paper, based on the notion of marginally stable modes of vector perturbations in the AdS soliton back ground we investigate the magnetic field effect on holographic $ p $- wave insulator/superconductor transition in the probe limit. We perform explicit analytic calculations considering both Schwarzschild AdS soliton and Gauss Bonnet AdS soliton back grounds and obtain a unique relation between the chemical potential and the magnetic field near the critical point. We also extend our analysis for $ p+ip $- wave back ground in the presence of external magnetic field. In both the cases it is observed that the non abelian model exhibit \textit{droplet} solutions. Moreover it is also found that the increase in the value of the external magnetic field essentially reduces the size of the droplet and thereby makes the condensation harder.

Analytical investigation of the phase transition between holographic insulator and superconductor in Gauss-Bonnet gravity

We employ the variational method for the Sturm-Liouville eigenvalue problem to analytically study the phase transition between the holographic insulator and superconductor in the Gauss-Bonnet gravity. By investigating the s-wave and p-wave holographic insulator/superconductor models, we find that this analytic method is more effective to obtain the analytic results on the condensation and the critical phenomena in the AdS soliton background in Gauss-Bonnet gravity. Our analytic result can be used to back up the numerical computations in the AdS soliton with Gauss-Bonnet correction.

Various types of phase transitions in the AdS soliton background

We study the basic holographic insulator and superconductor phase transition in the AdS soliton background by generalizing the spontaneous breaking of a global U(1) symmetry to occur via Stückelberg mechanism. We construct the soliton solutions with backreaction and examine the effects of the backreaction on the condensation of the scalar hair in the generalized Stückelberg Lagrangian. We disclose rich physics in various phase transitions. In addition to the AdS soliton configuration, we also examine the property of the phase transition in the AdS black hole background.

Integrability lost: Chaotic dynamics of classical strings on a confining holographic background

It is known that classical string dynamics on pure AdS5×S5 is integrable and plays an important role in solvability. This is a deep and central issue in holography. Here we investigate similar classical integrability for a more realistic confining background and provide a negative answer. The dynamics of a class of simple string configurations on AdS soliton background can be mapped to the dynamics of a set of non-linearly coupled oscillators. In a suitable limit of small fluctuations we discuss a quasi-periodic analytic solution of the system. Numerics indicates chaotic behavior as the fluctuations are not small. Integrability implies the existence of a regular foliation of the phase space by invariant manifolds. Our numerics shows how this nice foliation structure is eventually lost due to chaotic motion. We also verify a positive Lyapunov index for chaotic orbits. Our dynamics is roughly similar to other known non-integrable coupled oscillator systems like Hénon–Heiles equations.

Stability of the AdS Soliton Spacetime

Stability of the AdS Soliton Spacetime Gungwon Kang Korea Institute of Science and Technology Information, Daejeon 305-806 Changheon Ohy and Chul H. Leez Department of Physics and BK21 Division of Advanced Research and Education in Physics, Hanyang University, Seoul 133-791 (Received 21 August 2007) The AdS soliton spacetime is a vacuum static solution of ve-dimensional Einstein equations with a cosmological constant. It is asymptotically AdS and regular everywhere without having any curvature singularity or an event horizon inside. Recently, Horowitz and Myers conjectured that this spacetime is the ground state among all spacetime solutions that are asymptotically AdS. If such a conjecture is valid, the spacetime should be stable under small perturbations. We have investigated this issue by numerically studying the full nonlinear evolution of a certain class of perturbations. Our results show that some metric components decay out whereas one metric component grows, indicating a sort of instability. Motivated by this result, we also performed a linearized stability analysis for small perturbations in the same class. Interestingly, our result in such a linearized analysis does not show any indication of instability. Finally, we discuss the implications of our results on the stability of the AdS soliton background. PACS numbers: 04.25.Dm, 04.25.Nx, 04.65.+e