Integral geometry and holography

By B. Czech, L. Lamprou, Sam McCandlish, J. Sully. 2015

219 citations recorded by the source corpus.

A bstractWe present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts — points, distances and angles — are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.

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

View Paper: https://www.semanticscholar.org/paper/8a035d303ca5e6aa95b3dacd75283ba6f72f3538

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. D. Stanford
2. D. Harlow
3. J. Maldacena
4. T. Takayanagi
5. R. Myers
6. G. Turiaci
7. Tom Mertens
8. S. Raju

In Nuclear and High Energy Physics

1. D. Stanford
2. D. Harlow
3. J. Maldacena
4. Tom Mertens
5. R. Myers
6. T. Takayanagi
7. G. Turiaci
8. H. Verlinde

In Statistical and Nonlinear Physics

1. D. Stanford
2. D. Harlow
3. Tom Mertens
4. G. Turiaci
5. T. Takayanagi
6. S. Raju
7. J. Maldacena
8. R. Myers

Citations in the corpus

• Remarks on the Sachdev-Ye-Kitaev model (2016, background): “At low energies the extra dimension defined in this way has a metric characterized by the conformal group and can be viewed as a dS2 (or AdS2) space in accordance with recent discussions of kinematic space [29, 30].”
• Solving the Schwarzian via the conformal bootstrap (2017, methodology): “In the past few years it has been recognized that holographic CFTs at finite temperature exhibit characteristics of many body quantum chaos [1, 2, 3, 4, 5].”
• Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, background): “Secondly, in the tensor network description there is a subtle issue that the MERA network can also be interpreted as a de Sitter space [5, 9], while the refined tensor networks given in [8, 11] are argued to describe Euclidean hyperbolic spaces.”
• Shape dependence of entanglement entropy in conformal field theories (2015, unknown): “In theories with holographic duals, the RyuTakayanagi proposal maps this space into the space of mimimal-area surfaces in the bulk, and so the entanglement density provides a natural metric on the latter space as well (see [20] for more details in the AdS3/CFT2 case).”
• A stereoscopic look into the bulk (2016, methodology): “Recall that kinematic space and integral geometry emerged as essential tools for reconstructing the bulk geometry from entanglement entropies [9, 47].”
• Bit Threads and Holographic Entanglement (2016, background): “spacetime metric from the EEs of boundary regions (and a related quantity called “entwinement”) has been investigated recently by Czech and collaborators [33–35].”