Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHolographic Entropy Cone with Time Dependence in Two Dimensions
57
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In holographic duality, if a boundary state has a geometric description that realizes the Ryu-Takayanagi proposal then its entanglement entropies must obey certain inequalities that together define the so-called holographic entropy cone. A large family of such inequalities have been proven under the assumption that the bulk geometry is static, using a method involving contraction maps. By using kinematic space techniques, we show that in two boundary (three bulk) dimensions, all entropy inequalities that can be proven in the static case by contraction maps must also hold in holographic states with time dependence.
rate research
Read More
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.
We write down Crofton formulas--expressions that compute lengths of spacelike curves in asymptotically AdS$_3$ geometries as integrals over kinematic space--which apply when the curve and/or the background spacetime is time-dependent. Relative to their static predecessor, the time-dependent Crofton formulas display several new features, whose origin is the local null rotation symmetry of the bulk geometry. In pure AdS$_3$ where null rotations are global symmetries, the Crofton formulas simplify and become integrals over the null planes, which intersect the bulk curve.
Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic Entropy Cone (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the Quantum Extremal Surface (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI.
We construct Holographic Space-time models that reproduce the dynamics of $1 + 1$ dimensional string theory. The necessity for a dilaton field in the $1 + 1$ effective Lagrangian for classical geometry, the appearance of fermions, and even the form of the universal potential in the canonical $1$ matrix model, follow from general HST considerations. We note that t Hoofts ansatz for the leading contribution to the black hole S-matrix, accounts for the entire S-matrix in these models in the limit that the string scale coincides with the Planck scale, up to transformations between near horizon and asymptotic coordinates. These $1 + 1$ dimensional models are describable as decoupling limits of the near horizon geometry of higher dimensional extremal black holes or black branes, and this suggests that deformations of the simplest model are equally physical. After proposing a notion of relevant deformations, we describe deformations, which contain excitations corresponding to linear dilaton black holes, some of which can be considered as UV completions of the CGHS model. We study the question of whether the AMPS paradox can be formulated in those models. It cannot, because the classical in-fall time to the singularity of linear dilaton black holes, is independent of the black hole mass. This result is reproduced by our HST models. We argue that it is related to the absence of quasi-normal modes of these black hole solutions, which is itself related to the fact that the horizon has zero area. This is compatible with the resolution of the AMPS paradox proposed in previous work with Fischler, according to which the compatibility conditions of HST identify the long non-singular sojourn of observers behind the horizon, with the dynamics of equilibration on the horizon as seen by a detector which has not yet fallen through the horizon.
We study holographic entanglement entropy in Gauss-Bonnet gravity following a global quench. It is known that in dynamical scenarios the entanglement entropy probe penetrates the apparent horizon. The goal of this work is to study how far behind the horizon can the entanglement probe reach in a Gauss-Bonnet theory. We find that the behavior is quite different depending on the sign of the Gauss-Bonnet coupling $lambda_{GB}$. We show that for $lambda_{GB} > 0$ the holographic entanglement entropy probe explores less of the spacetime behind the horizon than in Einstein gravity. On the other hand, for $lambda_{GB} < 0$ the results are strikingly different; for early times a new family of solutions appears. These new solutions reach arbitrarily close to the singularity. We calculate the entanglement entropy for the two family of solutions with negative coupling and find that the ones that reach the singularity are the ones of less entropy. Thus, for $lambda_{GB} < 0$ the holographic entanglement entropy probes further behind the horizon than in Einstein gravity. In fact, for early times it can explore all the way to the singularity.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
