Holographic representation of local bulk operators

By A. Hamilton, D. Kabat, G. Lifschytz, D. Lowe. 2006

564 citations recorded by the source corpus.

The Lorentzian anti-de Sitter/conformal field theory correspondence implies a map between local operators in supergravity and nonlocal operators in the CFT. By explicit computation we construct CFT operators which are dual to local bulk fields in the semiclassical limit. The computation is done for general dimension in global, Poincare and Rindler coordinates. We find that the CFT operators can be taken to have compact support in a region of the complexified boundary whose size is set by the bulk radial position. We show that at finite N the number of independent commuting operators localized within a bulk volume saturates the holographic bound.

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

View Paper: https://www.semanticscholar.org/paper/b3e1164b7fb1b7e3695cf2f2b4336abf12e4b4da

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. Harlow
2. S. Raju
3. D. Stanford
4. J. Maldacena
5. Ahmed Almheiri
6. J. Polchinski
7. Zhenbin Yang
8. S. Shenker

In Nuclear and High Energy Physics

1. D. Harlow
2. S. Raju
3. D. Stanford
4. J. Maldacena
5. Ahmed Almheiri
6. R. Myers
7. Zhenbin Yang
8. D. Marolf

In Statistical and Nonlinear Physics

1. D. Harlow
2. S. Raju
3. D. Stanford
4. J. Maldacena
5. Ahmed Almheiri
6. Zhenbin Yang
7. Aitor Lewkowycz
8. D. Marolf

Citations in the corpus

• Wormholes, emergent gauge fields, and the weak gravity conjecture (2015, methodology): “The subject of reconstruction of bulk fields as boundary operators in AdS/CFT has generated a lot of interest in the last few years [1–5].”
• Shape dependence of entanglement entropy in conformal field theories (2015, unknown): “1 arises from an integral over an operator located inside the domain of dependence of A, which reminds us of smearing functions that are used to construct local bulk fields [49].”
• Lessons from the information paradox (2020, methodology): “Operators outside the black-hole horizon can be mapped to smeared CFT operators [179] using the standard HKLL method [180–183] or other equivalent methods [184,185].”
• Diving into traversable wormholes (2017, background): “Alternatively, it seems possible to use the HKLL [17] construction to produce a bulk operator localized near the horizon so that we can also use more massive fields, but we have not analyzed in detail the potential pitfalls of this strategy.”
• The Black Hole Information Problem (2016, background): “To give an explicit construction [55] for these precursors [56] (so-named because the timereversed case was considered first) or bulk fields, begin with the bulk equation of motion, e.”
• A stereoscopic look into the bulk (2016, methodology): “This is the same smeared representation of a bulk operator at the center of AdS3 as that found by HKLL [16].”
• Bulk locality and quantum error correction in AdS/CFT (2014, methodology): “We begin by briefly recalling the standard CFT construction of local bulk fields in AdS [1, 3, 14].”
• Deriving covariant holographic entanglement (2016, methodology): “35 This is true with the current technology modulo the subtlety that the HKLL procedure [35] involves a nonstandard Cauchy problem.”
• Holographic and Wilsonian renormalization groups (2010, background): “(The construction is similar to that of bulk fields in AdS [46], which also seems to be essentially Lorentzian.”
• Emergent spacetime and holographic CFTs (2011, background): “In this section we basically review statements made in [5], [6], [87], [8], [88], [89], [90].”
• Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime (2014, background): “Using the classical equations of motion, it is possible (at least perturbatively in the bulk coupling constants) to reconstruct the bulk state in WR from the bulk fields near DR [23, 58–66].”
• Local bulk operators in AdS/CFT: A holographic description of the black hole interior (2006, methodology): “In this paper we study this in detail, generalizing our earlier work [6, 7].”
• The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “• Subregion Duality: Given a subregion A of a boundary time-slice Σ, we are able to reconstruct any bulk operator φ(x) which is in the causal wedge of A, denoted CA and defined as the intersection of the bulk future and the bulk past of the boundary domain of dependence of A, as a CFT operator with ”
• The factorization problem in Jackiw-Teitelboim gravity (2018, background): “Most discussions of bulk physics in AdS/CFT focus on perturbative fields about a fixed background [1–8].”