Scanning the Parameter Space of Holographic Superconductors

We study various physical quantities associated with holographic s-wave superconductors as functions of the scaling dimensions of the dual condensates. A bulk scalar field with negative mass squared $m^2$, satisfying the Breitenlohner-Freedman stability bound and the unitarity bound, and allowed to vary in $0.5$ unit intervals, were considered. We observe that all the physical quantities investigated are sensitive to the scaling dimensions of the dual condensates. For all the $m^2$, the characteristic lengths diverge at the critical temperature in agreement with the Ginzburg-Landau theory. The Ginzburg-Landau parameter, obtained from these length scales indicates that the holographic superconductors can be type I or type II depending on the charge and the scaling dimensions of the dual condensates. For a fixed charge, there exists a critical scaling dimension, above which a holographic superconductor is type I, below which it becomes a type II.Comment: 24 pages 47 figure

The Coherent Crooks Equality

This chapter reviews an information theoretic approach to deriving quantum fluctuation theorems. When a thermal system is driven from equilibrium, random quantities of work are required or produced: the Crooks equality is a classical fluctuation theorem that quantifies the probabilities of these work fluctuations. The framework summarised here generalises the Crooks equality to the quantum regime by modeling not only the driven system but also the control system and energy supply that enables the system to be driven. As is reasonably common within the information theoretic approach but high unusual for fluctuation theorems, this framework explicitly accounts for the energy conservation using only time independent Hamiltonians. We focus on explicating a key result derived by Johan {\AA}berg: a Crooks-like equality for when the energy supply is allowed to exist in a superposition of energy eigenstates states.Comment: 11 pages, 3 figures; Chapter for the book "Thermodynamics in the Quantum Regime - Recent Progress and Outlook", eds. F. Binder, L. A. Correa, C. Gogolin, J. Anders and G. Adess

Coarse-Graining Can Beat the Rotating Wave Approximation in Quantum Markovian Master Equations

We present a first-principles derivation of the Markovian semi-group master equation without invoking the rotating wave approximation (RWA). Instead we use a time coarse-graining approach which leaves us with a free timescale parameter, which we can optimize. Comparing this approach to the standard RWA-based Markovian master equation, we find that significantly better agreement is possible using the coarse-graining approach, for a three-level model coupled to a bath of oscillators, whose exact dynamics we can solve for at zero temperature. The model has the important feature that the RWA has a non-trivial effect on the dynamics of the populations. We show that the two different master equations can exhibit strong qualitative differences for the population of the energy eigenstates even for such a simple model. The RWA-based master equation misses an important feature which the coarse-graining based scheme does not. By optimizing the coarse-graining timescale the latter scheme can be made to approach the exact solution much more closely than the RWA-based master equation

AdS/CFT with Flavour in Electric and Magnetic Kalb-Ramond Fields

We investigate gauge/gravity duals with flavour for which pure-gauge Kalb-Ramond B fields are turned on in the background, into which a D7 brane probe is embedded. First we consider the case of a magnetic field in two of the spatial boundary directions. We show that at finite temperature, i.e. in the AdS-Schwarzschild background, the B field has a stabilizing effect on the mesons and chiral symmetry breaking occurs for a sufficiently large value of the B field. Then we turn to the electric case of a B field in the temporal direction and one spatial boundary direction. In this case, there is a singular region in which it is necessary to turn on a gauge field on the brane in order to ensure reality of the brane action. We find that the brane embeddings are attracted towards this region. Far away from this region, in the weak field case at zero temperature, we investigate the meson spectrum and find a mass shift similar to the Stark effect.Comment: 34 pages, 18 figures, v2: added references and comments on mode decoupling, on thermodynamics and holographic renormalisation, JHEP style, v3: Final published versio

Energy Loss of Heavy Quarks from Asymptotically AdS Geometries

We investigate some universal features of AdS/CFT models of heavy quark energy loss. In addition, as a specific example, we examine quark damping in the spinning D3-brane solution dual to N=4 SU(N_c) super Yang-Mills at finite temperature and R-charge chemical potential.Comment: 17 pages, 9 figures; v2 refs added, typo fixe

Holographic Studies of Entanglement Entropy in Superconductors

We present the results of our studies of the entanglement entropy of a superconducting system described holographically as a fully back-reacted gravity system, with a stable ground state. We use the holographic prescription for the entanglement entropy. We uncover the behavior of the entropy across the superconducting phase transition, showing the reorganization of the degrees of freedom of the system. We exhibit the behaviour of the entanglement entropy from the superconducting transition all the way down to the ground state at T=0. In some cases, we also observe a novel transition in the entanglement entropy at intermediate temperatures, resulting from the detection of an additional length scale.Comment: 21 pages, 14 figures. v2:Clarified some remarks concerning stability. v3: Updated to the version that appears in JHE

Holographic Aspects of Fermi Liquids in a Background Magnetic Field

We study the effects of an external magnetic field on the properties of the quasiparticle spectrum of the class of 2+1 dimensional strongly coupled theories holographically dual to charged AdS$_4$ black holes at zero temperature. We uncover several interesting features. At certain values of the magnetic field, there are multiple quasiparticle peaks representing a novel level structure of the associated Fermi surfaces. Furthermore, increasing magnetic field deforms the dispersion characteristics of the quasiparticle peaks from non-Landau toward Landau behaviour. At a certain value of the magnetic field, just at the onset of Landau-like behaviour of the Fermi liquid, the quasiparticles and Fermi surface disappear.Comment: 18 pages, 10 figures. Revised some of the terminology: changed non-separable solutions to infinite-sum solution

Criticality, Scaling and Chiral Symmetry Breaking in External Magnetic Field

We consider a D7-brane probe of $AdS_{5}\times S^5$ in the presence of pure gauge $B$-field. The dual gauge theory is flavored Yang-Mills theory in external magnetic field. We explore the dependence of the fermionic condensate on the bare quark mass $m_{q}$ and study the discrete self-similar behavior of the theory near the origin of the parametric space. We calculate the critical exponents of the bare quark mass and the fermionic condensate. A study of the meson spectrum supports the expectation based on thermodynamic considerations that at zero bare quark mass the stable phase of the theory is a chiral symmetry breaking one. Our study reveals the self-similar structure of the spectrum near the critical phase of the theory, characterized by zero fermionic condensate and we calculate the corresponding critical exponent of the meson spectrum.Comment: 29 pages, 9 figures. Accepted in JHEP. Updated to mach the published version. One figure added, some definitions improve

Dynamics of Fundamental Matter in N=2* Yang-Mills Theory

We study the dynamics of quenched fundamental matter in $\mathcal{N}=2^\ast$ supersymmetric large $N$ SU(N) Yang-Mills theory at zero temperature. Our tools for this study are probe D7-branes in the holographically dual $\mathcal{N}=2^\ast$ Pilch-Warner gravitational background. Previous work using D3-brane probes of this geometry has shown that it captures the physics of a special slice of the Coulomb branch moduli space of the gauge theory, where the $N$ constituent D3-branes form a dense one dimensional locus known as the enhancon, located deep in the infrared. Our present work shows how this physics is supplemented by the physics of dynamical flavours, revealed by the D7-branes embeddings we find. The Pilch-Warner background introduces new divergences into the D7-branes free energy, which we are able to remove with a single counterterm. We find a family of D7-brane embeddings in the geometry and discuss their properties. We study the physics of the quark condensate, constituent quark mass, and part of the meson spectrum. Notably, there is a special zero mass embedding that ends on the enhancon, which shows that while the geometry acts repulsively on the D7-branes, it does not do so in a way that produces spontaneous chiral symmetry breaking.Comment: 24 pages, 8 figures. Corrected typos, added comment about counterterm. To appear in JHE