Generalized Superconductors and Holographic Optics - II

Using linear response theory, we analyze optical response properties of generalized holographic superconductors, in AdS-Schwarzschild and single R-charged black hole backgrounds in four dimensions. By introducing momentum dependent vector mode perturbations, the response functions for these systems are studied numerically, including the effects of backreaction. This complements and completes the probe limit analysis for these backgrounds initiated in our previous work ({\tt arXiv : 1305.6273}). Our numerical analysis indicates a negative Depine-Lakhtakia index for both the backgrounds studied, at low enough frequencies. The dependence of the response functions on the backreaction parameter and the model parameters are established and analyzed with respect to similar backgrounds in five dimensions.Comment: 1+26 Pages, 26 .eps figure

On the time dependence of holographic complexity in a dynamical Einstein-dilaton model

We study the holographic "complexity=action'" (CA) and "complexity=volume" (CV) proposals in Einstein-dilaton gravity in all spacetime dimensions. We analytically construct an infinite family of black hole solutions and use CA and CV proposals to investigate the time evolution of the complexity. Using the CA proposal, we find dimensional dependent violation of the Lloyd bound in early as well as in late times. Moreover, depending on the parameters of the theory, the bound violation relative to the conformal field theory result can be tailored in the early times as well. In contrast to the CA proposal, the CV proposal in our model yields results similar to those obtained in the literature.Comment: 33 pages, 27 figures, 1 table. Various typos corrected from the previous version, references and discussion added. Altered to match published versio

Confining gauge theories and holographic entanglement entropy with a magnetic field

We consider the soft wall model for a heuristic holographical modelling of a confining gauge theory and discuss how the introduction of a (constant) magnetic field influences the (de)confinement phase structure. We use the entanglement entropy as a diagnostic tool in terms of the length of an entangling strip geometry. Due to the anisotropy introduced by the magnetic field, we find that the results depend on the orientation of the strip relative to the field. This allows to identify a richer, anisotropic, interplay between confinement and a magnetic field than possibly can be extracted from a more standard order parameter as, for example, the Polyakov loop expectation value.Comment: 25 pages, 31 figure

Thermal entropy of a quark-antiquark pair above and below deconfinement from a dynamical holographic QCD model

We discuss the entropy carried by a quark-antiquark pair, in particular across the deconfinement transition. We therefore rely on a self-consistent solution to Einstein-Maxwell-dilaton gravity, capable of mimicking essential features of QCD. In particular we introduce a novel model that still captures well the QCD confinement and deconfinement phases, while allowing the introduction of a temperature in a phase which resembles the confined phase, this thanks to it being dual to a small black hole. We pay due attention to some subtleties of such a model. We confirm the lattice picture of a strong build-up of thermal entropy towards the critical temperature T-c, both coming from below or above T-c. We also include a chemical potential, confirming this entropic picture and we consider its effect on the speed of sound. Moreover, the temperature dependent confinement phase from the holography side allows us to find a string tension that does not vanish at T-c, a finding also supported by lattice QCD

Generalized Holographic Superconductors with Higher Derivative Couplings

We introduce and study generalized holographic superconductors with higher derivative couplings between the field strength tensor and a complex scalar field, in four dimensional AdS black hole backgrounds. We study this theory in the probe limit, as well as with backreaction. There are multiple tuning parameters in the theory, and with two non-zero parameters, we show that the theory has a rich phase structure, and in particular, the transition from the normal to the superconducting phase can be tuned to be of first order or of second order within a window of one of these. This is established numerically as well as by computing the free energy of the boundary theory. We further present analytical results for the critical temperature of the model, and compare these with numerical analysis. Optical properties of this system are also studied numerically in the probe limit, and our results show evidence for negative refraction at low frequencies.Comment: 1 + 27 pages, LaTeX, 24 .eps figures. References added, typos fixed, discussion on optical properties expanded. Version accepted in JHE

Generalized Superconductors and Holographic Optics

We study generalized holographic s-wave superconductors in four dimensional R-charged black hole and Lifshitz black hole backgrounds, in the probe limit. We first establish the superconducting nature of the boundary theories, and then study their optical properties. Numerical analysis indicates that a negative Depine-Lakhtakia index may appear at low frequencies in the theory dual to the R-charged black hole, for certain temperature ranges, for specific values of the charge parameter. The corresponding cut-off values for these are numerically established in several cases. Such effects are seen to be absent in the Lifshitz background where this index is always positive.Comment: 1 + 22 Pages, LaTeX, 18 .eps figures. Discussions expanded and results on Lifshitz backgrounds added. Published versio

Very General Holographic Superconductors and Entanglement Thermodynamics

We construct and analyze holographic superconductors with generalized higher derivative couplings, in single R-charged black hole backgrounds in four and five dimensions. These systems, which we call very general holographic superconductors, have multiple tuning parameters and are shown to exhibit a rich phase structure. We establish the phase diagram numerically as well as by computing the free energy, and then validated the results by calculating the entanglement entropy for these systems. The entanglement entropy is shown to be a perfect indicator of the phase diagram. The differences in the nature of the entanglement entropy in R-charged backgrounds compared to the AdS-Schwarzschild cases are pointed out. We also compute the analogue of the entangling temperature for a subclass of these systems and compare the results with non-hairy backgrounds.Comment: 1 + 32 pages, LaTeX, 27 .eps figure