Extremal surfaces as bulk probes in AdS/CFT

By V. Hubeny. 2012

190 citations recorded by the source corpus.

A bstractMotivated by the need for further insight into the emergence of AdS bulk spacetime from CFT degrees of freedom, we explore the behaviour of probes represented by specific geometric quantities in the bulk. We focus on geodesics and n-dimensional extremal surfaces in a general static asymptotically AdS spacetime with spherical and planar symmetry, respectively. While our arguments do not rely on the details of the metric, we illustrate some of our findings explicitly in spacetimes of particular interest (specifically AdS, Schwarzschild-AdS and extreme Reissner-Nordstrom-AdS). In case of geodesics, we find that for a fixed spatial distance between the geodesic endpoints, spacelike geodesics at constant time can reach deepest into the bulk. We also present a simple argument for why, in the presence of a black hole, geodesics cannot probe past the horizon whilst anchored on the AdS boundary at both ends. The reach of an extremal n-dimensional surface anchored on a given region depends on its dimensionality, the shape and size of the bounding region, as well as the bulk metric. We argue that for a fixed extent or volume of the boundary region, spherical regions give rise to the deepest reach of the corresponding extremal surface. Moreover, for physically sensible spacetimes, at fixed extent of the boundary region, higher-dimensional surfaces reach deeper into the bulk. Finally, we show that in a static black hole spacetime, no extremal surface (of any dimensionality, anchored on any region in the boundary) can ever penetrate the horizon.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7abbf600ec00e8db3d8da65f495be9d3d2bae553

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. T. Takayanagi
2. V. Hubeny
3. R. Myers
4. D. Harlow
5. M. Rangamani
6. Thomas Hartman
7. J. Maldacena
8. S. Raju

In Nuclear and High Energy Physics

1. T. Takayanagi
2. V. Hubeny
3. R. Myers
4. D. Harlow
5. M. Rangamani
6. Thomas Hartman
7. S. Raju
8. J. Maldacena

In Statistical and Nonlinear Physics

1. T. Takayanagi
2. D. Harlow
3. R. Myers
4. V. Hubeny
5. S. Raju
6. M. Rangamani
7. Mark Van Raamsdonk
8. Thomas Hartman

Citations in the corpus

• Bulk curves from boundary data in holography (2013, methodology): “generalization of (31) may oer a holographic interpretation of the focusing theorem [39]. The problem is related to identifying a holographic dual to a density matrix, which has been 14 discussed in [40, 41, 42, 43] (see also [44]). A helpful intermediate step might be to covariantize the proposal (”
• Causality & holographic entanglement entropy (2014, background): “extremal surfaces do not penetrate event horizons [17]; however this is no longer the case in dynamical situations [15, 16, 18–20].”
• Time evolution of entanglement entropy from black hole interiors (2013, background): “In a static situation, extremal surfaces do not penetrate the event horizon [3], but if the system is time dependent then it is possible to probe the interior.”
• Holographic geometry of entanglement renormalization in quantum field theories (2012, background): “Refer to [28, 29] for several developments in this direction.”
• The gravity dual of a density matrix (2012, background): “The wedge of minimal-area extremal surfaces w(DA) Based on these observations, and the observation of Hubeny that the extremal surfaces probe deepest into the bulk in various examples, it is natural to define a second candidate for the region R(A) based on extremal surfaces.”