State-Dependent Bulk-Boundary Maps and Black Hole Complementarity

By K. Papadodimas, S. Raju. 2013

267 citations recorded by the source corpus.

We provide a simple and explicit construction of local bulk operators that describe the interior of a black hole in the AdS/CFT correspondence. The existence of these operators is predicated on the assumption that the mapping of CFT operators to local bulk operators depends on the state of the CFT. We show that our construction leads to an exactly local effective field theory in the bulk. Barring the fact that their charge and energy can be measured at infinity, we show that the commutator of local operators inside and outside the black hole vanishes exactly, when evaluated within correlation functions of the CFT. Our construction leads to a natural resolution of the strong subadditivity paradox of Mathur and Almheiri et al. Furthermore, we show how, using these operators, it is possible to reconcile small corrections to effective field theory correlators with the unitarity of black hole evaporation. We address and resolve all other arguments, advanced in A. Almheiri et al. J. High Energy Phys. 09 (2013) 018 and D. Marolf and J. Polchinski, Phys. Rev. Lett. 111, 171301 (2013), in favor of structure at the black hole horizon. We extend our construction to states that are near equilibrium, and thereby also address the "frozen vacuum" objections of R. Bousso, Phys. Rev. Lett. 112, 041102 (2014). Finally, we explore an intriguing link between our construction of interior operators and Tomita-Takesaki theory.

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

View Paper: https://www.semanticscholar.org/paper/a0b398a5b7dd44c87413a4d22149a973d953d105

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. S. Raju
2. D. Harlow
3. D. Stanford
4. S. Shenker
5. J. Maldacena
6. H. Geng
7. A. Karch
8. R. Myers

In Nuclear and High Energy Physics

1. S. Raju
2. D. Harlow
3. D. Stanford
4. J. Maldacena
5. R. Myers
6. S. Shenker
7. A. Karch
8. Geoffrey Penington

In Statistical and Nonlinear Physics

1. S. Raju
2. D. Harlow
3. D. Stanford
4. S. Shenker
5. Geoffrey Penington
6. T. Faulkner
7. K. Papadodimas
8. J. Maldacena

Citations in the corpus

• Remarks on the necessity and implications of state-dependence in the black hole interior (2015, methodology): “The semi-classical origins of state-dependence that (3)In this paper we adopt notation that is consistent with [8, 9].”
• Black Hole Remnants and the Information Loss Paradox (2014, background): “String theoretic approaches, à la Papadodimas-Raju [37–40], of probing the interior of black holes may eventually offer some clues.”
• Jerusalem Lectures on Black Holes and Quantum Information (2014, background): “So far no version of A = RB has appeared which can give completely satisfying resolutions to these objections; the proposal that comes closest is that of Raju and Papadodimas [165, 166], which among other things is able to “postpone” the commutator problem to operations that involve some order one f”
• Wormholes, emergent gauge fields, and the weak gravity conjecture (2015, background): “In particular the additional subtleties present when there are gauge symmetries in the bulk has recently received a fair bit of attention [6–15].”
• Entwinement and the emergence of spacetime (2014, unknown): “This conundrum reflects a general difficulty in the AdS/CFT correspondence of identifying field theoretic observables associated to physics in a region of size less than one AdS volume [20, 21, 22, 23, 24, 25, 26, 27].”
• A general proof of the quantum null energy condition (2017, background): “a nite dimensional Hilbert space this condition would be equivalent to the statement that the reduced density matrix ˆ A (for a nite quantum system A = ˆ A ˆ 1 A ) has full rank and so is invertible [59], { 14 { however it will be important to acknowledge the fact that in an innite quantum system, s”
• TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, background): “This idea first appeared in [55], who wanted to use it as part of a (controversial [56, 57, 58]) proposal to reconstruct the interiors of generic black hole microstates.”
• Inconsistency of islands in theories with long-range gravity (2021, background): “Excitations of the island in the region outside the black hole horizon correspond to the “near-equilibrium” states of [79].”
• Entanglement wedge reconstruction and the information paradox (2019, background): “The idea that there does not exist any single boundary operator that always corresponds to a given interior bulk operator, and instead different boundary operators must be used for different states, goes back to Papadodidimas and Raju [32, 33].”
• The Holographic Nature of Null Infinity (2020, background): “This resolution is, of course, not new and the same as the resolution suggested by the ideas of black hole complementarity [44, 45, 46] and ER=EPR [47].”
• Multiple shocks (2013, background): “Roughly, the action of Wn(tn) disturbs the delicate tuning required for a local perturbation to appear at time tn−1; in (14)The “mirror operators” of [35] might be candidates for these.”
• Lessons from the information paradox (2020, methodology): “The construction of interior operators that we describe here was developed in [17, 51, 176].”