108 research outputs found
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
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