27 research outputs found

### Entanglement negativity, Holography and Black holes

We investigate the application of our recent holographic entanglement
negativity conjecture for higher dimensional conformal field theories to
specific examples which serve as crucial consistency checks. In this context we
compute the holographic entanglement negativity for bipartite pure and finite
temperature mixed state configurations in $d$-dimensional conformal field
theories dual to bulk pure $AdS_{d+1}$ geometry and $AdS_{d+1}$-Schwarzschild
black holes respectively. It is observed that the holographic entanglement
negativity characterizes the distillable entanglement for the finite
temperature mixed states through the elimination of the thermal contributions.
Significantly our examples correctly reproduce universal features of the
entanglement negativity for corresponding two dimensional conformal field
theories, in higher dimensions.Comment: 32 pages, 3 figures, minor modification

### Holographic entanglement negativity for disjoint intervals in $AdS_3/CFT_2$

We advance a holographic construction for the entanglement negativity of
bipartite mixed state configurations of two disjoint intervals in $(1+1)$
dimensional conformal field theories ($CFT_{1+1}$) through the $AdS_3/CFT_2$
correspondence. Our construction constitutes the large central charge analysis
of the entanglement negativity for mixed states under consideration and
involves a specific algebraic sum of bulk space like geodesics anchored on
appropriate intervals in the dual $CFT_{1+1}$. The construction is utilized to
compute the holographic entanglement negativity for such mixed states in
$CFT_{1+1}$s dual to bulk pure $AdS_3$ geometries and BTZ black holes
respectively. Our analysis exactly reproduces the universal features of
corresponding replica technique results in the large central charge limit which
serves as a consistency check.Comment: 17 pages, 4 figure

### Fast Scrambling of Mutual Information in Kerr-AdS$_4$

We compute the disruption of mutual information between the hemispherical
subsystems on the left and right CFT$s$ of a Thermofield Double state described
by a Kerr geometry in $AdS_4$ due to shockwaves along the equatorial plane. The
shockwaves and the subsystems considered respect the axi-symmetry of the
geometry. At late times the disruption of the mutual information is given by
the lengthening of the HRT surface connecting the two subsystems, we compute
the minimum value of the Lyapunov index-$\lambda_L^{(min)}$ at late times and
find that it is bounded by $\kappa=\frac{2\pi T_H}{(1-\mu\, \mathcal{L})}$
where $\mu$ is the horizon velocity and $\mathcal{L}$ is the angular momentum
per unit energy of the shockwave. At very late times we find the the scrambling
time for such a system is governed by $\kappa$ with $\kappa t_*=\log
\mathcal{S}$ for large black holes with large entropy $\mathcal{S}$. We also
find a term that increases the scrambling time by
$\log(1-\mu\,\mathcal{L})^{-1}$ but which does not scale with the entropy of
the Kerr geometry.Comment: 21-pages, 4-figure

### State Dependence of Krylov Complexity in $2d$ CFTs

We compute the Krylov Complexity of a light operator $\mathcal{O}_L$ in an
eigenstate of a $2d$ CFT at large central charge $c$. The eigenstate
corresponds to a primary operator $\mathcal{O}_H$ under the state-operator
correspondence. We observe that the behaviour of K-complexity is different
(either bounded or exponential) depending on whether the scaling dimension of
$\mathcal{O}_H$ is below or above the critical dimension $h_H=c/24$, marked by
the $1st$ order Hawking-Page phase transition point in the dual $AdS_3$
geometry. Based on this feature, we hypothesize that the notions of operator
growth and K-complexity for primary operators in $2d$ CFTs are closely related
to the underlying entanglement structure of the state in which they are
computed, thereby demonstrating explicitly their state-dependent nature. To
provide further evidence for our hypothesis, we perform an analogous
computation of K-complexity in a model of free massless scalar field theory in
$2d$, and in the integrable $2d$ Ising CFT, where there is no such transition
in the spectrum of states.Comment: 24 pages, 5 figures, minor corrections, references adde