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

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

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

p-Wave holographic superconductors with Weyl corrections

We study the (3+1) dimensional p-wave holographic superconductors with Weyl corrections both numerically and analytically. We describe numerically the behavior of critical temperature $T_{c}$ with respect to charge density $\rho$ in a limited range of Weyl coupling parameter $\gamma$ and we find in general the condensation becomes harder with the increase of parameter $\gamma$. In strong coupling limit of Yang-Mills theory, we show that the minimum value of $T_{c}$ obtained from analytical approach is in good agreement with the numerical results, and finally show how we got remarkably a similar result in the critical exponent 1/2 of the chemical potential $\mu$ and the order parameter$$ with the numerical curves of superconductors.Comment: 7 pages, 1 figure, 1 table. One refrence added, presentations improve

Landau Levels, Magnetic Fields and Holographic Fermi Liquids

We further consider a probe fermion in a dyonic black hole background in anti-de Sitter spacetime, at zero temperature, comparing and contrasting two distinct classes of solution that have previously appeared in the literature. Each class has members labeled by an integer n, corresponding to the n-th Landau level for the fermion. Our interest is the study of the spectral function of the fermion, interpreting poles in it as indicative of quasiparticles associated with the edge of a Fermi surface in the holographically dual strongly coupled theory in a background magnetic field H at finite chemical potential. Using both analytical and numerical methods, we explicitly show how one class of solutions naturally leads to an infinite family of quasiparticle peaks, signaling the presence of a Fermi surface for each level n. We present some of the properties of these peaks, which fall into a well behaved pattern at large n, extracting the scaling of Fermi energy with n and H, as well as the dispersion of the quasiparticles.Comment: 23 pages, 4 figures. Changed some of the terminology: non-separable -> infinite-sum. Clarified the relationship between our ansatz and the separable ansat

Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches

We study the evolution and scaling of the entanglement entropy after two types of quenches for a 2+1 field theory, using holographic techniques. We study a thermal quench, dual to the addition of a shell of uncharged matter to four dimensional Anti-de Sitter (AdS_4) spacetime, and study the subsequent formation of a Schwarzschild black hole. We also study an electromagnetic quench, dual to the addition of a shell of charged sources to AdS_4, following the subsequent formation of an extremal dyonic black hole. In these backgrounds we consider the entanglement entropy of two types of geometries, the infinite strip and the round disc, and find distinct behavior for each. Some of our findings naturally supply results analogous to observations made in the literature for lower dimensions, but we also uncover several new phenomena, such as (in some cases) a discontinuity in the time derivative of the entanglement entropy as it nears saturation, and for the electromagnetic quench, a logarithmic growth in the entanglement entropy with time for both the disc and strip, before settling to saturation.Comment: 30 pages, 19 figures. Corrected typos and added some discussion. To appear in New J. Phy

Surprising Connections Between General Relativity and Condensed Matter

This brief review is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity.Comment: 14 pages; based on talk given at GR1

Chiral Symmetry Breaking and External Fields in the Kuperstein-Sonnenschein Model

A novel holographic model of chiral symmetry breaking has been proposed by Kuperstein and Sonnenschein by embedding non-supersymmetric probe D7 and anti-D7 branes in the Klebanov-Witten background. We study the dynamics of the probe flavours in this model in the presence of finite temperature and a constant electromagnetic field. In keeping with the weakly coupled field theory intuition, we find the magnetic field promotes spontaneous breaking of chiral symmetry whereas the electric field restores it. The former effect is universally known as the "magnetic catalysis" in chiral symmetry breaking. In the presence of an electric field such a condensation is inhibited and a current flows. Thus we are faced with a steady-state situation rather than a system in equilibrium. We conjecture a definition of thermodynamic free energy for this steady-state phase and using this proposal we study the detailed phase structure when both electric and magnetic fields are present in two representative configurations: mutually perpendicular and parallel.Comment: 50 pages, multiple figures, minor typo fixed, references adde

Flavoured Large N Gauge Theory in an External Magnetic Field

We consider a D7-brane probe of AdS$_{5}\times S^5$ in the presence of pure gauge $B$-field. In the dual gauge theory, the $B$-field couples to the fundamental matter introduced by the D7-brane and acts as an external magnetic field. The $B$-field supports a 6-form Ramond-Ramond potential on the D7-branes world volume that breaks the supersymmetry and enables the dual gauge theory to develop a non-zero fermionic condensate. We explore the dependence of the fermionic condensate on the bare quark mass $m_{q}$ and show that at zero bare quark mass a chiral symmetry is spontaneously broken. A study of the meson spectrum reveals a coupling between the vector and scalar modes, and in the limit of weak magnetic field we observe Zeeman splitting of the states. We also observe the characteristic $\sqrt{m_{q}}$ dependence of the ground state corresponding to the Goldstone boson of spontaneously broken chiral symmetry.Comment: 22 pages, 7 figures, references added, few typos correcte