Black brane steady states

We follow the evolution of an asymptotically AdS black brane with a fixed temperature gradient at spatial infinity until a steady state is formed. The resulting energy density and energy flux of the steady state in the boundary theory are compared to a conjecture on the behavior of steady states in conformal field theories. Very good agreement is found.Comment: 8 pages, 3 figures. References added, typos correcte

Universal chiral conductivities for low temperature holographic superfluids

We argue that the chiral conductivities of generic s-wave holographic superfluids, whose broken U(1) symmetry is anomalous, exhibit universal behavior at low temperatures. The universal behavior we argue for is independent of the details of the bulk action and on the emergent geometry deep in the bulk interior at low temperatures. Our results are contrasted against general expectations based on an analysis of the entropy current in superfluids.Comment: 14 pages, 2 figure

Probing emergent geometry through phase transitions in free vector and matrix models

Boundary correlation functions provide insight into the emergence of an effective geometry in higher spin gravity duals of O(N) or U(N) symmetric field theories. On a compact manifold, the singlet constraint leads to nontrivial dynamics at finite temperature and large N phase transitions even at vanishing 't Hooft coupling. At low temperature, the leading behavior of boundary two-point functions is consistent with propagation through a bulk thermal anti de Sitter space. Above the phase transition, the two-point function shows significant departure from thermal AdS space and the emergence of localized black hole like objects in the bulk. In adjoint models, these objects appear at length scales of order of the AdS radius, consistent with a Hawking-Page transition, but in vector models they are parametrically larger than the AdS scale. In low dimensions, we find another crossover at large distances beyond which the correlation function again takes a thermal AdS form, albeit with a temperature dependent normalization factor.Comment: 24 pages, 1 table, 3 figure

Residues of Correlators in the Strongly Coupled N=4 Plasma

Quasinormal modes of asymptotically AdS black holes can be interpreted as poles of retarded correlators in the dual gauge theory. To determine the response of the system to small external perturbations it is not enough to know the location of the poles: one also needs to know the residues. We compute them for R-charge currents and find that they are complex except for the hydrodynamic mode, whose residue is purely imaginary. For different quasinormal modes the residue grows with momentum q, whereas for the hydrodynamic mode it behaves as a damped oscillation with distinct zeroes at finite q. Similar to collective excitations at weak coupling the hydrodynamic mode decouples at short wavelengths. Knowledge of the residues allows as well to define the time scale t_H from when on the system enters the hydrodynamic regime, restricting the validity of hydrodynamic simulations to times t>t_H.Comment: 10 pages, 3 figures, revtex4, v2: improved exposition and figure

AdS black holes as reflecting cavities

We use the identification between null singularities of correlators in the bulk with time singularities in the boundary correlators to study the analytic structure of time-dependent thermal Green functions using the eikonal approximation for classical solutions in the AdS black hole background. We show that the location of singularities in complex time can be understood in terms of null rays bouncing on the boundaries and singularities of the eternal black hole, giving the picture of a `reflecting cavity'. We can then extract the general analytic expression for the asymptotic values of the frequencies of quasinormal modes in large AdS black holes.Comment: 14 pages, 2 figures, reference adde

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 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

Holographic Superfluids and the Landau Criterion

We revisit the question of stability of holographic superfluids with finite superfluid velocity. Our method is based on applying the Landau criterion to the Quasinormal Mode (QNM) spectrum. In particular we study the QNMs related to the Goldstone modes of spontaneous symmetry breaking with linear and quadratic dispersions.In the linear case we show that the sound velocity becomes negative for large enough superfluid velocity and that the imaginary part of the quasinormal frequency moves to the upper half plane. Since the instability is strongest at finite wavelength, we take this as an indication for the existence of an inhomogeneous or striped condensed phase for large superfluid velocity. In the quadratic case the instability is present for arbitrarily small superfluid velocity.Comment: 26 pages, 10 Figures; v2: authors's name corrected, reference adde

Retículos de subgrupos

Traballo Fin de Grao en Matemáticas. Curso 2019-2020[GL] O obxectivo deste traballo é facer unha incursión na teoría de retículos para dar resposta a algunhas preguntas tales como que relacións hai entre a estrutura dun grupo G e a do seu retículo de subgrupos L(G), centrándonos especialmente nos grupos finitos. Para iso, introduciremos previamente algúns conceptos elementais da teoría básica de retículos, á que lle dedicaremos os primeiros capítulos. A relación máis básica que atopamos é que os isomorfismos entre grupos inducen isomorfismos entre os seus retículos de subgrupos, pero non á inversa. A segunda parte do traballo dedicarase a preguntas máis complexas como determinar se hai grupos asociados a unha clase de retículos. Buscaremos en dúas clases de retículos: os retículos distributivos e os retículos modulares. Finalmente, presentaremos exemplos de grupos que están determinados polo seu retículo de subgrupos.[EN] The purpose of this work is to make a foray into lattice theory to answer some questions such that what are the relationships between the structure of a group G and that of its subgroup lattice L(G), focusing especially on finite groups. In order to do this, we will previously introduce some elementary concepts of basic lattice theory, to which we will dedicate the first chapters. The most basic relationship we find is that isomorphisms between groups induce isomorphisms between their subgroup lattices, but not the other way around. The second part of the work will be devoted to more complex questions such as determining whether there are groups associated with a lattice class. We will look at two lattice classes: distributive lattice and modular lattice. Finally, we will introduce examples of groups that are determined by their subgroup lattice