Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space. (English) Zbl 1361.81112

Summary: We study a two-dimensional dilaton gravity system, recently examined by Almheiri and Polchinski, which describes near-extremal black holes, or more generally, nearly \(A d S_2\) spacetimes. The asymptotic symmetries of \(A d S_2\) are all the time reparametrizations of the boundary. These symmetries are spontaneously broken by the \(A d S_2\) geometry and they are explicitly broken by the small deformation away from \(A d S_2\). 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.


81T25 Quantum field theory on lattices
81R40 Symmetry breaking in quantum theory
83E30 String and superstring theories in gravitational theory
83C57 Black holes
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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