Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space

2016/06/06 by Juan Maldacena, Douglas Stanford, Maldacena, Juan +3 · 2 voices · 39 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.1606.01857

Abstract

We study a two dimensional dilaton gravity system, recently examined by Almheiri and Polchinski, which describes near extremal black holes, or more generally, nearly AdS₂ spacetimes. The asymptotic symmetries of AdS₂ are all the time reparametrizations of the boundary. These symmetries are spontaneously broken by the AdS₂ geometry and they are explicitly broken by the small deformation away from AdS₂. 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.

Citations

• Les Houches Lectures on Black Holes

Cited by

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• Two dimensional de-Sitter and deformed CFTs
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• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal
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• Many-body chaos and pole-skipping in holographic charged rotating fluids
• Islands and traversable wormholes
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• Logarithmic Corrections to Thermodynamics of Accelerating Black Holes
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• Quantum corrected black hole microstates and entropy
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• The Effects of Near-AdS₂ Backreaction on Matter Fields
• Hamiltonian approach to near-extremal black hole evaporation and backreaction
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Discussions

• The linearized Schwarzian action is a quadratic Euclidean action $^1$ $$\begin{align} I[\epsilon]~=~&\frac{1}{2}\int_{-\pi}^{\pi}\!du~\left( \epsilon^{\prime\prime 2}-\epsilon^{\prime2}\right)\cr ~\st [stackexchange, 8 points]
• I am reading a paper arXiv:1606.01857 . This paper expand the Schwarzian action (3.18) with a perturbation $$ \tau=u+\epsilon(u).\tag{4.26} $$ Then the linearized action becomes $$ I=\frac{C}{2}\int d [stackexchange, 5 points]

Related

• Conformal boundaries near extremal black holes
• Black Hole Entropy and the Pseudo Goldstone Bosons of Conformal Symmetry
• Asymptotic Isometry and Two Dimensional Anti-de Sitter Gravity
• AdS₃ gravity and the complex SYK models
• Chaos and the reparametrization mode on the AdS₂ string