Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space
Open accessAbstract
We study a two-dimensional dilaton gravity system, recently examined by Almheiri and Polchinski, which describes near-extremal black holes, or more generally, nearly AdS 2 spacetimes.The asymptotic symmetries of AdS 2 are all the time reparametrizations of the boundary.These symmetries are spontaneously broken by the AdS 2 geometry and they are explicitly broken by the small deformation away from AdS 2 .This pattern of spontaneous plus explicit symmetry breaking governs the gravitational backreaction of the system.It determines several gravitational properties such as the linear in temperature dependence of the near-extremal entropy as well as the gravitational corrections to correlation functions.These corrections include the ones determining the growth of out-of-time-order correlators that is indicative of chaos.These gravitational aspects can be described in terms of a Schwarzian derivative effective action for a reparametrization..........
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In the δ → 0 limit the outgoing shockwave decouples from the ingoing shockwave, simplifying the conformal welding problem, and then the Euclidean equations reduce exactly to the 'boundary particle' equations for the Schwarzian theory studied in [1,41,42].
“In the δ → 0 limit the outgoing shockwave decouples from the ingoing shockwave -this simplifies the conformal welding problem, and then the Euclidean equations reduce exactly to the 'boundary particle' equations for the Schwarzian theory studied in [1,41,42].”
From Replica wormholes for an evaporating 2D black hole (2021) · cites this paper as [41]
Split into 2 atoms — 1 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredThe Lorentzian methods of [1,41,42] and the Euclidean approach of [13] are in perfect agreement, resolving the puzzle that Lorentzian methods led to simple local dynamics whereas the Euclidean approach requires non-local conformal welding.
“At this point we have resolved one of the puzzles described in the introduction: the Lorentzian methods of [1,41,42] led to relatively simple, local dynamics, whereas the Euclidean approach of [13] requires non-local solutions of the conformal welding problem.We have shown that these two methods are in perfect agreement.”
From Replica wormholes for an evaporating 2D black hole (2021) · cites this paper as [41]
Section 2.2 describes a Euclidean formulation with boundary reparametrizations, so the paper supports identifying it as an Euclidean approach. Our copy does not describe that approach as requiring non-local conformal welding; the non-local action discussed in the Additional information section concerns a different setting. The assertion that the two methods agree is the citing authors’ own conclusion, not a claim attributed to this source. (LLM, conf=0.84)
Experimental — accuracy not yet measuredWe recover the Lorentzian equation of motion from [41,42] when the only outgoing matter is that coming from Hawking radiation, as opposed to the explicit outgoing shockwave.
“In other words, we recover the Lorentzian equation of motion from [41,42] when the only outgoing matter is that coming from Hawking radiation, as opposed to the explicit outgoing shockwave.”
From Replica wormholes for an evaporating 2D black hole (2021) · cites this paper as [41]
Section 4, “Adding matter” (Eq. 4.1), gives an equation for the boundary trajectory with a massless-matter energy flux, and Section 6.2 discusses an explicit shock-wave solution. Our copy does not identify the outgoing flux in that equation as Hawking radiation or state the claimed Hawking-radiation-only case. (LLM, conf=0.82)
Experimental — accuracy not yet measuredThe boundary particle equations of motion used in [1,41,42] correspond to a limit where the no-mixing condition is satisfied, so that the welding problem can be solved exactly and used to write simple Lorentzian equations.
“The boundary particle equations of motion used in [1,41,42] correspond to a limit where the no-mixing condition is satisfied, so that the welding problem can be solved exactly and used to write simple Lorentzian equations.”
From Replica wormholes for an evaporating 2D black hole (2021) · cites this paper as [41]
Section 4, “Adding matter” (eq. 4.1), gives an equation for the boundary trajectory, and p. 12/26 discusses the Lorentzian action. Our copy does not state that these equations arise in a no-mixing limit or that a welding problem can be solved exactly; searches for “no-mixing” and “welding” found no such passage. (LLM, conf=0.84)
Experimental — accuracy not yet measuredIn JT gravity, the dilaton equations of motion in conformal gauge are (5.17).
“the dilaton equations of motion in JT gravity are [41”
From Replica wormholes for an evaporating 2D black hole (2021) · cites this paper as [41]
Section 3 (p. 5/26) gives the JT action and the dilaton equation obtained by varying the metric, numbered (3.3). Section 2.1 gives conformally flat AdS₂ coordinates, but our copy does not present the cited equation specifically in conformal gauge or as equation (5.17). (LLM, conf=0.82)
Experimental — accuracy not yet measured
In JT gravity, a local bulk theory gives rise to a degree of freedom associated with asymptotic boundaries, described by the Schwarzian path integral.
“In that theory, a local bulk theory gives rise to a degree JHEP08(2020)044 of freedom associated with asymptotic boundaries, described by the Schwarzian path integral [94,95].”
From Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020) · cites this paper as [94]
The scaling limit reproduces the local Lorentzian equations for the Schwarzian 'boundary particle' derived in [41,42] and studied in AEMM [1].
“This turns out to reproduce the local Lorentzian equations for the Schwarzian 'boundary particle' derived in [41,42] and studied in AEMM [1].”
From Replica wormholes for an evaporating 2D black hole (2021) · cites this paper as [41]
The dynamics of x(t) are governed by the Schwarzian action.
“The dynamics of x(t) are governed by the Schwarzian action.”
From Replica wormholes for an evaporating 2D black hole (2021) · cites this paper as [41]
Both the SYK model and simple nearly-AdS2 gravity theories such as Jackiw-Teitelboim gravity have an emergent reparameterisation symmetry that is both spontaneously and explicitly broken, with explicit symmetry-breaking term proportional to the Schwarzian action.
“Although the precise dual gravity description, if one exists, remain unknown, both the SYK model and simple nearly-AdS 2 JHEP09(2020)002 gravity theories such as Jackiw-Teitelboim gravity [73, 95-98] have an emergent reparameterisation symmetry that is both spontaneously and explicitly broken, with the explicit symmetry-breaking term proportional to the so-called Schwarzian action”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [98]
In this problem, θ(τ) arises as the reparametrization mode, or boundary graviton, of the nearly AdS2 gravity theory.
“In our problem, θ ( τ ) arises as the reparametrization mode, or 'boundary graviton' of the nearlyAdS 2 gravity theory”
From Replica wormholes and the entropy of Hawking radiation (2020) · cites this paper as [47]
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- Authors
- Maldacena, J., Stanford, D., & Yang, Z.
- Affiliations
- Institute for Advanced Study (US)
- Princeton University (US)
- Corresponding author
- Maldacena, Juan
- Venue
- Progress of Theoretical and Experimental Physics
- Publisher
- Oxford University Press (OUP)
- Published
- 2016-11-10
- Volume
- 2016
- Issue
- 12
- Pages
- 12C104
- ISSN
- 2050-3911 (ISSN-L)
- OpenAlex
- W2415090955
- Cited by
- 1,068
- References
- 40
- Citations by year
- 2026: 65 · 2025: 93 · 2024: 91 · 2023: 129 · 2022: 118 · 2021: 146 · 2020: 135 · 2019: 129 · 2018: 89 · 2017: 69 · 2016: 4
- FWCI
- 46.88
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- other-oa
- Locations
- Progress of Theoretical and Experimental Physics (publishedVersion, other-oa)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion, other-oa)
- HighWire Press Open Archive (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (DESC0009988)
- Simons Foundation (385600)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- conformal symmetry breaking, two-dimensional dilaton gravity, near-extremal black holes, asymptotic symmetries, time reparametrization, spontaneous symmetry breaking, explicit symmetry breaking, gravitational backreaction, out-of-time-order correlators, chaos, AdS2
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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