A
bstract
We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not ...only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent (
λ
L
) and butterfly velocity (
v
B
), independently of the symmetry breaking patterns. We show that the diffusion constant (
D
) is bounded by
D
≥
v
B
2
/
λ
L
, where
D
is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit.
A
bstract
We study the holographic duality between the reflected entropy and the entanglement wedge cross section with the first order correction. In the field theory side, we consider the reflected ...entropy for
ρ
AB
m
, where
ρ
AB
is the reduced density matrix for two intervals in the ground state. The reflected entropy in the 2d holographic conformal field theories is computed perturbatively up to the first order in
m −
1 by using the semiclassical conformal block. In the gravity side, we compute the entanglement wedge cross section in the backreacted geometry by cosmic branes with tension
T
m
which are anchored at the AdS boundary. Comparing both results we find a perfect agreement, showing the duality works with the first order correction in
m −
1.
Classifying pole-skipping points Ahn, Yong jun; Jahnke, Viktor; Jeong, Hyun-Sik ...
The journal of high energy physics,
03/2021, Letnik:
2021, Številka:
3
Journal Article
Recenzirano
Odprti dostop
A
bstract
We clarify general mathematical and physical properties of pole-skipping points. For this purpose, we analyse scalar and vector fields in hyperbolic space. This setup is chosen because it ...is simple enough to allow us to obtain analytical expressions for the Green’s function and check everything explicitly, while it contains all the essential features of pole-skipping points. We classify pole-skipping points in three types (type-I, II, III). Type-I and Type-II are distinguished by the (limiting) behavior of the Green’s function near the pole-skipping points. Type-III can arise at non-integer
iω
values, which is due to a specific UV condition, contrary to the types I and II, which are related to a non-unique near horizon boundary condition. We also clarify the relation between the pole-skipping structure of the Green’s function and the near horizon analysis. We point out that there are subtle cases where the near horizon analysis alone may not be able to capture the existence and properties of the pole-skipping points.
A
bstract
Motivated by the recent connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators (OTOCs), we study the pole structure of thermal ...two-point functions in
d
-dimensional conformal field theories (CFTs) in hyperbolic space. We derive the pole-skipping points of two-point functions of scalar and vector fields by three methods (one field theoretic and two holographic methods) and confirm that they agree. We show that the leading pole-skipping point of two point functions is related with the late time behavior of conformal blocks and shadow conformal blocks in four-point OTOCs.
A
bstract
Homes’ law,
ρ
s
=
Cσ
DC
T
c
, is a universal relation of superconductors between the superfluid density
ρ
s
at zero temperature, the critical temperature
T
c
and the electric DC ...conductivity
σ
DC
at
T
c
. Experimentally, Homes’ law is observed in high
T
c
superconductors with linear-
T
resistivity in the normal phase, giving a material independent universal constant
C
. By using holographic models related to the Gubser-Rocha model, we investigate how Homes’ law can be realized together with linear-
T
resistivity in the presence of momentum relaxation. We find that strong momentum relaxation plays an important role to exhibit Homes’ law with linear-
T
resistivity.
We study the entanglement entropy (EE) and the Rényi entropy (RE) of multiple intervals in two-dimensional TT¯- deformed conformal field theory (CFT) at a finite temperature by field theoretic and ...holographic methods. First, by the replica method with the twist operators, we construct the general formula of the RE and EE up to the first order of a deformation parameter. By using our general formula, we show that the EE of multiple intervals for a holographic CFT is just a summation of the single interval case even with the small deformation. This is a nontrivial consequence from the field theory perspective, though it may be expected by the Ryu-Takayanagi formula in holography. However, the deformed RE of the two intervals is a summation of the single interval case only if the separations between the intervals are big enough. It can be understood by the tension of the cosmic branes dual to the RE. We also study the holographic EE for single and two intervals with an arbitrary cutoff radius (dual to the TT¯ deformation) at any temperature. We confirm our holographic results agree with the field theory results with a small deformation and high temperature limit, as expected. For two intervals, there are two configurations for EE: disconnected (s-channel) and connected (t-channel) ones. We investigate the phase transition between them as we change parameters: as the deformation or temperature increases the phase transition is suppressed and the disconnected phase is more favored.
A
bstract
We revisit the magneto-hydrodynamics in (2+1) dimensions and confirm that it is consistent with the quasi-normal modes of the (3+1) dimensional dyonic black holes in the most general set-up ...with finite density, magnetic field and wave vector. We investigate all possible modes (sound, shear, diffusion, cyclotron etc.) and their interplay. For the magneto-hydrodynamics we perform a complete and detailed analysis correcting some prefactors in the literature, which is important for the comparison with quasi-normal modes. For the quasi-normal mode computations in holography we identify the independent fluctuation variables of the dyonic black holes, which is nontrivial at finite density and magnetic field. As an application of the quasi-normal modes of the dyonic black holes we investigate a transport property, the diffusion constant. We find that the diffusion constant at finite density and magnetic field saturates the lower bound at low temperature. We show that this bound can be understood from the pole-skipping point.
A
bstract
We investigate the breakdown of magneto-hydrodynamics at low temperature (
T
) with black holes whose extremal geometry is AdS
2
×R
2
. The breakdown is identified by the equilibration ...scales (
ω
eq
, k
eq
) defined as the collision point between the diffusive hydrodynamic mode and the longest-lived non-hydrodynamic mode. We show (
ω
eq
, k
eq
) at low
T
is determined by the diffusion constant
D
and the scaling dimension ∆(0) of an infra-red operator:
ω
eq
= 2
πT
∆(0)
,
k
eq
2
=
ω
eq
/D
, where ∆(0) = 1 in the presence of magnetic fields. For the purpose of comparison, we have analytically shown ∆(0) = 2 for the axion model independent of the translational symmetry breaking pattern (explicit or spontaneous), which is complementary to previous numerical results. Our results support the conjectured universal upper bound of the energy diffusion
D
≤
ω
eq
/
k
eq
2
≔
v
eq
2
τ
eq
where
v
eq
:=
ω
eq
/k
eq
and
τ
eq
:=
ω
eq
−
1
are the velocity and the timescale associated to equilibration, implying that the breakdown of hydrodynamics sets the upper bound of the diffusion constant
D
at low
T
.
A
bstract
We investigate the properties of the holographic entanglement entropy of the systems in which the U(1) or the translational symmetry is broken
spontaneously
. For this purpose, we define ...the entanglement density of the strip-subsystems and examine both the first law of entanglement entropy (FLEE) and the area theorem. We classify the conditions that FLEE and/or the area theorem obey and show that such a classification may be useful for characterizing the systems. We also find universalities from both FLEE and the area theorem. In the spontaneous symmetry breaking case, FLEE is always obeyed regardless of the type of symmetry: U(1) or translation. For the translational symmetry, the area theorem is always violated when the symmetry is weakly broken, independent of the symmetry breaking patterns (explicit or spontaneous). We also argue that the log contribution of the entanglement entropy from the Goldstone mode may not appear in the strongly coupled systems.
PDF
