66 research outputs found
Supergoop Dynamics
We initiate a systematic study of the dynamics of multi-particle systems with
supersymmetric Van der Waals and electron-monopole type interactions. The
static interaction allows a complex continuum of ground state configurations,
while the Lorentz interaction tends to counteract this configurational fluidity
by magnetic trapping, thus producing an exotic low temperature phase of matter
aptly named supergoop. Such systems arise naturally in gauge
theories as monopole-dyon mixtures, and in string theory as collections of
particles or black holes obtained by wrapping D-branes on internal space
cycles. After discussing the general system and its relation to quiver quantum
mechanics, we focus on the case of three particles. We give an exhaustive
enumeration of the classical and quantum ground states of a probe in an
arbitrary background with two fixed centers. We uncover a hidden conserved
charge and show that the dynamics of the probe is classically integrable. In
contrast, the dynamics of one heavy and two light particles moving on a line
shows a nontrivial transition to chaos, which we exhibit by studying the
Poincar\'e sections. Finally we explore the complex dynamics of a probe
particle in a background with a large number of centers, observing hints of
ergodicity breaking. We conclude by discussing possible implications in a
holographic context.Comment: 35 pages,11 figures. v2: updated references to include a previous
proof of classical integrability, exchanged a figure for a prettier versio
Bosonic Fractionalisation Transitions
At finite density, charge in holographic systems can be sourced either by
explicit matter sources in the bulk or by bulk horizons. In this paper we find
bosonic solutions of both types, breaking a global U(1) symmetry in the former
case and leaving it unbroken in the latter. Using a minimal bottom-up model we
exhibit phase transitions between the two cases, under the influence of a
relevant operator in the dual field theory. We also embed solutions and
transitions of this type in M-theory, where, holding the theory at constant
chemical potential, the cohesive phase is connected to a neutral phase of
Schr\"odinger type via a z=2 QCP.Comment: references added. minor changes. version published in JHE
Phase transition and hyperscaling violation for scalar Black Branes
We investigate the thermodynamical behavior and the scaling symmetries of the
scalar dressed black brane (BB) solutions of a recently proposed, exactly
integrable Einstein-scalar gravity model [1], which also arises as
compactification of (p-1)-branes with a smeared charge. The extremal, zero
temperature, solution is a scalar soliton interpolating between a conformal
invariant AdS vacuum in the near-horizon region and a scale covariant metric
(generating hyperscaling violation on the boundary field theory)
asymptotically. We show explicitly that for the boundary field theory this
implies the emergence of an UV length scale (related to the size of the brane),
which decouples in the IR, where conformal invariance is restored. We also show
that at high temperatures the system undergoes a phase transition. Whereas at
small temperature the Schwarzschild-AdS BB is stable, above a critical
temperature the scale covariant, scalar-dressed BB solution, becomes
energetically preferred. We calculate the critical exponent z and the
hyperscaling violation parameter of the scalar-dressed phase. In particular we
show that the hyperscaling violation parameter is always negative. We also show
that the above features are not a peculiarity of the exact integrable model of
Ref.[1], but are a quite generic feature of Einstein-scalar and
Einstein-Maxwell-scalar gravity models for which the squared-mass of the scalar
field is positive and the potential vanishes exponentially as the scalar field
goes to minus infinity.Comment: 20 pages, 4 figures. In the revised version it has been pointed out
that the Einstein-scalar gravity model considered in the paper also arises as
compactification of black p-branes with smeared charge
Entangled Dilaton Dyons
Einstein-Maxwell theory coupled to a dilaton is known to give rise to
extremal solutions with hyperscaling violation. We study the behaviour of these
solutions in the presence of a small magnetic field. We find that in a region
of parameter space the magnetic field is relevant in the infra-red and
completely changes the behaviour of the solution which now flows to an
attractor. As a result there is an extensive ground state
entropy and the entanglement entropy of a sufficiently big region on the
boundary grows like the volume. In particular, this happens for values of
parameters at which the purely electric theory has an entanglement entropy
growing with the area, , like which is believed to be a
characteristic feature of a Fermi surface. Some other thermodynamic properties
are also analysed and a more detailed characterisation of the entanglement
entropy is also carried out in the presence of a magnetic field. Other regions
of parameter space not described by the end point are also
discussed.Comment: Some comments regarding comparison with weakly coupled Fermi liquid
changed, typos corrected and caption of a figure modifie
Quantum critical lines in holographic phases with (un)broken symmetry
All possible scaling IR asymptotics in homogeneous, translation invariant
holographic phases preserving or breaking a U(1) symmetry in the IR are
classified. Scale invariant geometries where the scalar extremizes its
effective potential are distinguished from hyperscaling violating geometries
where the scalar runs logarithmically. It is shown that the general critical
saddle-point solutions are characterized by three critical exponents (). Both exact solutions as well as leading behaviors are exhibited.
Using them, neutral or charged geometries realizing both fractionalized or
cohesive phases are found. The generic global IR picture emerging is that of
quantum critical lines, separated by quantum critical points which correspond
to the scale invariant solutions with a constant scalar.Comment: v3: 32+29 pages, 2 figures. Matches version published in JHEP.
Important addition of an exponent characterizing the IR scaling of the
electric potentia
Aspects of holography for theories with hyperscaling violation
We analyze various aspects of the recently proposed holographic theories with
general dynamical critical exponent z and hyperscaling violation exponent
. We first find the basic constraints on from the gravity
side, and compute the stress-energy tensor expectation values and scalar
two-point functions. Massive correlators exhibit a nontrivial exponential
behavior at long distances, controlled by . At short distance, the
two-point functions become power-law, with a universal form for .
Next, the calculation of the holographic entanglement entropy reveals the
existence of novel phases which violate the area law. The entropy in these
phases has a behavior that interpolates between that of a Fermi surface and
that exhibited by systems with extensive entanglement entropy. Finally, we
describe microscopic embeddings of some metrics into full
string theory models -- these metrics characterize large regions of the
parameter space of Dp-brane metrics for . For instance, the theory of
N D2-branes in IIA supergravity has z=1 and over a wide range
of scales, at large .Comment: 35 pages; v2: new references added; v3: proper reference [14] added;
v4: minor clarification
Schr\"odinger Holography with and without Hyperscaling Violation
We study the properties of the Schr\"odinger-type non-relativistic holography
for general dynamical exponent z with and without hyperscaling violation
exponent \theta. The scalar correlation function has a more general form due to
general z as well as the presence of \theta, whose effects also modify the
scaling dimension of the scalar operator. We propose a prescription for minimal
surfaces of this "codimension 2 holography," and demonstrate the (d-1)
dimensional area law for the entanglement entropy from (d+3) dimensional
Schr\"odinger backgrounds. Surprisingly, the area law is violated for d+1 < z <
d+2, even without hyperscaling violation, which interpolates between the
logarithmic violation and extensive volume dependence of entanglement entropy.
Similar violations are also found in the presence of the hyperscaling
violation. Their dual field theories are expected to have novel phases for the
parameter range, including Fermi surface. We also analyze string theory
embeddings using non-relativistic branes.Comment: 62 pages and 6 figures, v2: several typos in section 5 corrected,
references added, v3: typos corrected, references added, published versio
Holographic Entanglement Entropy and Fermi Surfaces
The entanglement entropy in theories with a Fermi surface is known to produce
a logarithmic violation of the usual area law behavior. We explore the
possibility of producing this logarithmic violation holographically by
analyzing the IR regions of the bulk geometries dual to such theories. The
geometry of Ogawa, Takayanagi, and Ugajin is explored and shown to have a null
curvature singularity for all values of parameters, except for dynamical
critical exponent 3/2 in four dimensions. The results are extended to general
hyperscaling violation exponent. We explore strings propagating through the
singularity and show that they become infinitely excited, suggesting the
singularity is not resolved by stringy effects and may become a full-fledged
"stringularity." An Einstein-Maxwell-dilaton embedding of the nonsingular
geometry is exhibited where the dilaton asymptotes to a constant in the IR. The
unique nonsingular geometry in any given number of dimensions is proposed as a
model to study the T=0 limit of a theory with a Fermi surface.Comment: 20 pages plus appendices, 5 figures; v2 discussion clarified, results
generalized, and acknowledgments update
Holographic Vitrification
We establish the existence of stable and metastable stationary black hole
bound states at finite temperature and chemical potentials in global and planar
four-dimensional asymptotically anti-de Sitter space. We determine a number of
features of their holographic duals and argue they represent structural
glasses. We map out their thermodynamic landscape in the probe approximation,
and show their relaxation dynamics exhibits logarithmic aging, with aging rates
determined by the distribution of barriers.Comment: 100 pages, 25 figure
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