60 research outputs found
Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model
In this note we investigate the anomalous breaking of anisotropic scaling
symmetry in a non-relativistic field theory with dynamical exponent z=2. On
general grounds, one can show that there exist two possible "central charges"
which characterize the breaking of scale invariance. Using heat kernel methods,
we compute these two central charges in the quantum Lifshitz model, a free
field theory which is second order in time and fourth order in spatial
derivatives. We find that one of the two central charges vanishes.
Interestingly, this is also true for strongly coupled non-relativistic field
theories with a geometric dual described by a metric and a massive vector
field.Comment: 26 pages; major revision (results were unaffected), published versio
Analytic Lifshitz black holes in higher dimensions
We generalize the four-dimensional R^2-corrected z=3/2 Lifshitz black hole to
a two-parameter family of black hole solutions for any dynamical exponent z and
for any dimension D. For a particular relation between the parameters, we find
the first example of an extremal Lifshitz black hole. An asymptotically
Lifshitz black hole with a logarithmic decay is also exhibited for a specific
critical exponent depending on the dimension. We extend this analysis to the
more general quadratic curvature corrections for which we present three new
families of higher-dimensional D>=5 analytic Lifshitz black holes for generic
z. One of these higher-dimensional families contains as critical limits the z=3
three-dimensional Lifshitz black hole and a new z=6 four-dimensional black
hole. The variety of analytic solutions presented here encourages to explore
these gravity models within the context of non-relativistic holographic
correspondence.Comment: 14 page
Deformations of Lifshitz holography
The simplest gravity duals for quantum critical theories with z=2 `Lifshitz'
scale invariance admit a marginally relevant deformation. Generic black holes
in the bulk describe the field theory with a dynamically generated momentum
scale Lambda as well as finite temperature T. We describe the thermodynamics of
these black holes in the quantum critical regime where T >> Lambda^2. The
deformation changes the asymptotics of the spacetime mildly and leads to
intricate UV sensitivities of the theory which we control perturbatively in
Lambda^2/T.Comment: 1+27 pages, 12 figure
Lovelock-Lifshitz Black Holes
In this paper, we investigate the existence of Lifshitz solutions in Lovelock
gravity, both in vacuum and in the presence of a massive vector field. We show
that the Lovelock terms can support the Lifshitz solution provided the
constants of the theory are suitably chosen. We obtain an exact black hole
solution with Lifshitz asymptotics of any scaling parameter in both
Gauss-Bonnet and in pure 3rd order Lovelock gravity. If matter is added in the
form of a massive vector field, we also show that Lifshitz solutions in
Lovelock gravity exist; these can be regarded as corrections to Einstein
gravity coupled to this form of matter. For this form of matter we numerically
obtain a broad range of charged black hole solutions with Lifshitz asymptotics,
for either sign of the cosmological constant. We find that these asymptotic
Lifshitz solutions are more sensitive to corrections induced by Lovelock
gravity than are their asymptotic AdS counterparts. We also consider the
thermodynamics of the black hole solutions and show that the temperature of
large black holes with curved horizons is proportional to where is
the critical exponent; this relationship holds for black branes of any size. As
is the case for asymptotic AdS black holes, we find that an extreme black hole
exists only for the case of horizons with negative curvature. We also find that
these Lovelock-Lifshitz black holes have no unstable phase, in contrast to the
Lovelock-AdS case. We also present a class of rotating Lovelock-Lifshitz black
holes with Ricci-flat horizons.Comment: 26 pages, 10 figures, a few references added, typo fixed and some
comments have been adde
Pathologies in Asymptotically Lifshitz Spacetimes
There has been significant interest in the last several years in studying
possible gravitational duals, known as Lifshitz spacetimes, to anisotropically
scaling field theories by adding matter to distort the asymptotics of an AdS
spacetime. We point out that putative ground state for the most heavily studied
example of such a spacetime, that with a flat spatial section, suffers from a
naked singularity and further point out this singularity is not resolvable by
any known stringy effect. We review the reasons one might worry that
asymptotically Lifshitz spacetimes are unstable and employ the initial data
problem to study the stability of such systems. Rather surprisingly this
question, and even the initial value problem itself, for these spacetimes turns
out to generically not be well-posed. A generic normalizable state will evolve
in such a way to violate Lifshitz asymptotics in finite time. Conversely,
enforcing the desired asymptotics at all times puts strong restrictions not
just on the metric and fields in the asymptotic region but in the deep interior
as well. Generically, even perturbations of the matter field of compact support
are not compatible with the desired asymptotics.Comment: 36 pages, 1 figure, v2: Enhanced discussion of singularity, including
relationship to Gubser's conjecture and singularity in RG flow solution, plus
minor clarification
Gauss-Bonnet Black Holes and Heavy Fermion Metals
We consider charged black holes in Einstein-Gauss-Bonnet Gravity with
Lifshitz boundary conditions. We find that this class of models can reproduce
the anomalous specific heat of condensed matter systems exhibiting
non-Fermi-liquid behaviour at low temperatures. We find that the temperature
dependence of the Sommerfeld ratio is sensitive to the choice of Gauss-Bonnet
coupling parameter for a given value of the Lifshitz scaling parameter. We
propose that this class of models is dual to a class of models of
non-Fermi-liquid systems proposed by Castro-Neto et.al.Comment: 17 pages, 6 figures, pdfLatex; small corrections to figure 10 in this
versio
Holography of Charged Dilaton Black Holes
We study charged dilaton black branes in . Our system involves a
dilaton coupled to a Maxwell field with dilaton-dependent
gauge coupling, . First, we find the solutions for
extremal and near extremal branes through a combination of analytical and
numerical techniques. The near horizon geometries in the simplest cases, where
, are Lifshitz-like, with a dynamical exponent
determined by . The black hole thermodynamics varies in an interesting
way with , but in all cases the entropy is vanishing and the specific
heat is positive for the near extremal solutions. We then compute conductivity
in these backgrounds. We find that somewhat surprisingly, the AC conductivity
vanishes like at T=0 independent of . We also explore the
charged black brane physics of several other classes of gauge-coupling
functions . In addition to possible applications in AdS/CMT, the
extremal black branes are of interest from the point of view of the attractor
mechanism. The near horizon geometries for these branes are universal,
independent of the asymptotic values of the moduli, and describe generic
classes of endpoints for attractor flows which are different from .Comment: 33 pages, 3 figures, LaTex; v2, references added; v3, more refs
added; v4, refs added, minor correction
Universal thermal and electrical conductivity from holography
It is known from earlier work of Iqbal, Liu (arXiv:0809.3808) that the
boundary transport coefficients such as electrical conductivity (at vanishing
chemical potential), shear viscosity etc. at low frequency and finite
temperature can be expressed in terms of geometrical quantities evaluated at
the horizon. In the case of electrical conductivity, at zero chemical potential
gauge field fluctuation and metric fluctuation decouples, resulting in a
trivial flow from horizon to boundary. In the presence of chemical potential,
the story becomes complicated due to the fact that gauge field and metric
fluctuation can no longer be decoupled. This results in a nontrivial flow from
horizon to boundary. Though horizon conductivity can be expressed in terms of
geometrical quantities evaluated at the horizon, there exist no such neat
result for electrical conductivity at the boundary. In this paper we propose an
expression for boundary conductivity expressed in terms of geometrical
quantities evaluated at the horizon and thermodynamical quantities. We also
consider the theory at finite cutoff outside the horizon (arXiv:1006.1902) and
give an expression for cutoff dependent electrical conductivity, which
interpolates smoothly between horizon conductivity and boundary conductivity .
Using the results about the electrical conductivity we gain much insight into
the universality of thermal conductivity to viscosity ratio proposed in
arXiv:0912.2719.Comment: An appendix added discussing relation between boundary conductivity
and universal conductivity of stretched horizon, version to be published in
JHE
Black holes and black branes in Lifshitz spacetimes
We construct analytic solutions describing black holes and black branes in
asymptotically Lifshitz spacetimes with arbitrary dynamical exponent z and for
arbitrary number of dimensions. The model considered consists of Einstein
gravity with negative cosmological constant, a scalar, and N U(1) gauge fields
with dilatonic-like couplings. We study the phase diagrams and thermodynamic
instabilities of the solution, and find qualitative differences between the
cases with 12.Comment: 27 pages, 10 figures; v2 references added, minor comments adde
Holographic Renormalization for Asymptotically Lifshitz Spacetimes
A variational formulation is given for a theory of gravity coupled to a
massive vector in four dimensions, with Asymptotically Lifshitz boundary
conditions on the fields. For theories with critical exponent z=2 we obtain a
well-defined variational principle by explicitly constructing two actions with
local boundary counterterms. As part of our analysis we obtain solutions of
these theories on a neighborhood of spatial infinity, study the asymptotic
symmetries, and consider different definitions of the boundary stress tensor
and associated charges. A constraint on the boundary data for the fields
figures prominently in one of our formulations, and in that case the only
suitable definition of the boundary stress tensor is due to Hollands,
Ishibashi, and Marolf. Their definition naturally emerges from our requirement
of finiteness of the action under Hamilton-Jacobi variations of the fields. A
second, more general variational principle also allows the Brown-York
definition of a boundary stress tensor.Comment: 34 pages, Added Reference
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