On geodesic propagators and black hole holography

By Jorma Louko, D. Marolf, S. Ross. 2000

199 citations recorded by the source corpus.

One of the most challenging technical aspects of the dualities between string theory on anti--de Sitter spaces and conformal field theories is understanding how location in the interior of spacetime is represented in the field theory. It has recently been argued that the interior of the spacetime can be directly probed by using intrinsically non-local quantities in the field theory. In addition, Balasubramanian and Ross [Phys. Rev. D 61, 044009 (2000)] argued that when the spacetime described the formation of an ${\mathrm{AdS}}_{3}$ black hole, the propagator in the field theory probed the whole spacetime, including the region behind the horizon. We use the same approach to study the propagator for the BTZ black hole and a black hole solution with a single exterior region, and show that it reproduces the propagator associated with the natural vacuum states on these spacetimes. We compare our result with a toy model of the CFT for the single-exterior black hole, finding remarkable agreement. The spacetimes studied in this work are analytic, which makes them quite special. We also discuss the interpretation of this propagator in more general spacetimes, shedding light on certain issues involving causality, black hole horizons, and products of local operators on the boundary.

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

View Paper: https://www.semanticscholar.org/paper/de69efbe068072344f7d6c5368e0f7d0ce3cb494

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In Astronomy and Astrophysics

1. D. Harlow
2. V. Hubeny
3. D. Stanford
4. R. Myers
5. L. Susskind
6. M. Rangamani
7. S. Shenker
8. J. Maldacena

In Nuclear and High Energy Physics

1. D. Harlow
2. D. Stanford
3. R. Myers
4. V. Hubeny
5. J. Maldacena
6. L. Susskind
7. S. Shenker
8. T. Takayanagi

In Statistical and Nonlinear Physics

1. D. Harlow
2. D. Stanford
3. R. Myers
4. V. Hubeny
5. S. Shenker
6. S. Raju
7. L. Susskind
8. J. Maldacena

Citations in the corpus

• Localized shocks (2014, methodology): “These include two-sided correlation functions [1, 2, 3], mutual information and entropy [4, 5, 6], and the pullbackpushforward [7, 8] modification of the standard smearing function procedure [9, 10, 11, 12].”
• Complexity and Shock Wave Geometries (2014, background): “see section 2.2) can be used as a clock, but it reaches its maximum after a multiple of the light-crossing time [1][2]. The decay of local correlation between the left and right CFTs may also be used [3][4][5]. These correlations exponentially decay for a time of order S, but then become noisy with ”
• The black hole singularity in AdS/CFT (2003, methodology): “A number of authors have explored ways to extract behind the horizon information from boundary correlators [28, 29 ,30,31,32].1 In”
• Extremal surfaces as bulk probes in AdS/CFT (2012, methodology): “h the bulk, this correlator is sensitive to the corresponding region of the bulk geometry. This was used to identify the CFT signature of the black hole singularity [14,15], building on prior work of [16,17,18], by considering the insertion points x and yon two disconnected boundaries corresponding ”
• Bulk and transhorizon measurements in AdS/CFT (2012, background): “[53] that these observables cannot be used to make the kind of quantum measurement that we are discussing.”
• The gravity dual of a density matrix (2012, background): “24 Don Marolf has pointed out to us that the connection between two-point functions and the lengths of spatial geodesics has been argued to fail for spacetimes that do not satisfy certain analyticity properties [15].”
• Entanglement of local operators in large-N conformal field theories (2014, unknown): “he geodesic between the operator’s insertion points that we schematically denoted xand x′. Our approximation should be valid for a general class of CFTs at large central charge c. We further refer to [36] for a discussions on validity and subtleties of (99). In formulas below we will not use Φ∆’s an”
• Causal holographic information (2012, background): “24 The importance of assuming analyticity was stressed in particular in [34].”
• Multiple shocks (2013, background): “In the bulk it is related to geodesics and hence probes the geometry [14, 15, 16, 17, 18, 19].”
• Black holes and the butterfly effect (2013, background): “This fact has been previously exploited for the purposes of studying black hole interiors [38, 39, 40, 41, 42, 43].”
• Causality & holographic entanglement entropy (2014, background): “, [51] for an earlier discussion of this issue).”
• Inflation in AdS/CFT (2005, methodology): “In this case one can write down explicit formulas for boundary correlators that continue from AdS/CFT to dS/CFT.”