Anomalous Transport in Holographic Chiral Superfluids via Kubo Formulae

We study anomalous conductivities in Chiral Superfluids in the framework of two different holographic models, by means of Kubo formulae. In addition, we point out the existence of an anomalous transport phenomenon that consists in the presence of a charge density when the superfluid velocity is aligned with a magnetic field. It has been pointed out recently that certain chiral conductivities in holographic superfluids exhibit universal behavior at zero temperature. We show that anomalous conductivities always stabilize at low temperatures in our setup. Even though the particular value they acquire is model-dependent, it seems to be robust and determined solely by the interplay between the broken symmetries and the anomalies.Comment: 23 pages, 22 figures. v2: references added, minor typos corrected. v3: footnotes added; published versio

Human development and inequality in the 20th Century : the Mercosur countries in a comparative perspective

This article is in line with the United Nations attempts to approach human development in wider terms than per capita GDP, and in line with an ever lively debate on the historical standard of living and on the role of inequality in development. We focus on three Mercosur countries (Argentina, Brazil and Uruguay) and we view them in comparison with four core countries (France, Germany, USA and UK) along the 20th Century. The paper makes different attempts to construct diverse indices and to change the weights of their different components in order to better explain human development in different periods. A contribution of the paper, so long limited to Uruguay and the USA, is to adjust the historical human development index by inequality measures for all of its components. The results show that Argentine started to diverge, even in human development, at early stages of the 20th Century; that Uruguay diverged from the mid-century and that Brazil continued to tighten the gap up to 1980, diverging afterwards without being able to come close to the levels of the core countries. Total inequality in Uruguay and USA showed similar levels and trends: it decreased until the 1950s, and increased afterwards to similar levels. While inequality affects human development within both countries, it doesn?t help to understand the differences between them, due to the mentioned similarity of the Gini-coefficients

Applications of holography to condensed matter Physics

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 11-09-2014We carry out a computation of chiral conductivities at strong coupling using holographic methods in Part II. To that end we implement chiral and mixed anomalies in the bulk by the use of suitable Chern-Simons terms. Then we study the cuto ow of anomalous conductivities by computing them at a hypersurface placed at certain radial position in spacetime, which models the energy cuto . Furthermore, we construct and analyze the holographic version of a two-component super uid. A two-component super uid has U(2) ! U(1) as the pattern of spontaneously broken symmetries and presents typically non-relativistic Goldstone bosons in its spectrum of excitations (the so-called type II Goldstone modes). We compute conductivities and dispersion relations for the hydrodynamic modes of the theory, as well as the gap of the so-called "massive Goldstone", a massive excitation that has been predicted to have a universal gap. Moreover, motivated by the presence of type II Goldstone bosons, we perform an analysis of the well-known Landau Criterion in the framework of our holographic models, showing that it holds. In addition, we construct a s+p-super uid, which features coexisting scalar and vector condensates. We also study its phase diagram after switching on two chemical potentials. Finally, we compute anomalous conductivities for U(1) holographic super uids. Along the way we also point out that there is charge density present whenever the super uid velocity is aligned with an external magnetic eld. This e ect absent if the theory is non-anomalous. The outcome of our calculation is that all chiral conductivities seem to approach universal values at zero temperature, even though they are not universal at - nite temperature. Such a universal value depends only on the interplay between broken symmetries and the anomaly.Llevamos a cabo un cálculo de conductividades quirales en acoplamiento fuerte utilizando métodos holográficos en la Parte II. Para ello implementamos las anomalías quiral y mixta en el bulk utilizando los términos de Chern-Simons adecuados. A continuación se estudia el flujo de las conductividades anómalas en función de una escala de energía, calculándolas en una hipersuperficie colocada a cierto valor de la coordenada radial en el espacio-tiempo, que modela dicho cutoff de energía. Además, construimos y analizamos la versión holográfica de un superfl uido de dos componentes. Un superfl uido de dos componentes tiene U(2) ! U(1) como patrón de simetrías espontáneamente rotas y presenta bosones de Goldstone tipicamente no relativistas en su espectro de excitaciones (los llamados modos de Goldstone de tipo II). Calculamos conductividades y relaciones de dispersión para los modos de hidrodinámicos de la teoría, así como la masa del llamado "Goldstone masivo", una excitación que se ha predicho que posee una masa universal. Por otra parte, motivado por la presencia de bosones de Goldstone de tipo II, llevamos a cabo un estudio del conocido Criterio de Landau en el marco de nuestros modelos holográficos, demostrando que se cumple. Además, se construye un superfl uido s+p, que se caracteriza por tener condensados escalar y vectorial coexistentes. También estudiamos el diagrama de fase tras encender dos potenciales químicos. Por último, calculamos conductividades anómalas para superfl uidos holográficas U(1). En el proceso también enfatizamos la existencia de una densidad de carga presente siempre que la supervelocidad esté alineada con un campo magnético externo. Este efecto está ausente si la teoría no es anómala. El resultado de nuestro cálculo se resume en que todas las conductividades quirales parecen aproximarse a valores universales a temperatura cero, a pesar de que no son universales a temperatura fínita. Dicho valor universal sólo depende de la interacción entre las simetrías rotas y la(s) anomalía(s

Holographic s+p Superconductors

We study the phase diagram of a holographic model realizing a U(2) global symmetry on the boundary and show that at low temperature a phase with both scalar s and vector p condensates exists. This is the s+p-wave phase where the global U(2) symmetry and also the spatial rotational symmetry are spontaneously broken. By studying the free energy we show that this phase is preferred when it exists. We also consider unbalanced configurations where a second chemical potential is turned on. They present a rich phase diagram characterized by the competition and coexistence of the s and p order parameters.Comment: 6 pages, 4 figures; v3: published version, clarifications and references adde

Holographic quenches and anomalous transport

We study the response of the chiral magnetic effect due to continuous quenches induced by time dependent electric fields within holography. Concretely, we consider a holographic model with dual chiral anomaly and compute the electric current parallel to a constant, homogeneous magnetic field and a time dependent electric field in the probe approximation. We explicitly solve the PDEs by means of pseudospectral methods in spatial and time directions and study the transition to an universal "fast" quench response. Moreover, we compute the amplitudes, i.e.,~residues of the quasi normal modes, by solving the (ODE) Laplace transformed equations. We investigate the possibility of considering the asymptotic growth rate of the amplitudes as a well defined notion of initial time scale for linearized systems. Finally, we highlight the existence of Landau level resonances in the electrical conductivity parallel to a magnetic field at finite frequency and show explicitly that these only appear in presence of the anomaly. We show that the existence of these resonances induces, among others, a long-lived AC electric current once the electric field is switched off.Comment: 34 pages, 10 figure

Holographic Type II Goldstone bosons

The Goldstone theorem implies the appearance of an ungapped mode whenever a continuous global symmetry is spontaneously broken. In general it does not say anything about the precise form of the dispersion relation nor does it imply that there is one massless mode for each broken symmetry generator. It is a well-established fact that even for relativistic field theories in the presence of a chemical potential Goldstone modes with quadratic dispersion relation, the type II Goldstone bosons, appear in the spectrum. We develop two holographic models that feature type II Goldstone modes as part of the quasinormal mode spectrum. The models are based on simple generalizations with U(2) symmetry of the well-studied holographic s-wave superfluid. Our results include Goldstone modes without broken generators but with unusual realization of symmetries and a frequency dependent conductivity of striking resemblance to the one of Graphene.Comment: 47 pages, 21 figures; v2: references and clarifications added, typos correcte