Abstract
In light of recent developments in nearly AdS2 holography, we revisit the semiclassical version of two-dimensional dilaton gravity proposed by Callan, Giddings, Harvey, and Strominger (CGHS) [1] in the early 90’s. In distinction to the classical model, the quantum-corrected CGHS model has an AdS2 vacuum with a constant dilaton. By turning on a non-normalizable mode of the Liouville field, i.e. the conformal mode of the 2d gravity, the explicit breaking of the scale invariance renders the AdS2 vacuum nearly AdS2. As a consequence, there emerges an effective one-dimensional Schwarzian-type theory of pseudo Nambu-Goldstone mode-the boundary graviton-on the boundary of the nearly AdS2 space. We go beyond the linear order perturbation in non-normalizable fluctuations of the Liouville field and work up to the second order. As a main result of our analysis, we clarify the role of the boundary graviton in the holographic framework and show the Virasoro/Schwarzian correspondence, namely that the 2d bulk Virasoro constraints are equivalent to the graviton equation of motion of the 1d boundary theory, at least, on the SL(2, R) invariant vacuum.
Highlights
As a main result of our analysis, we clarify the role of the boundary graviton in the holographic framework and show the Virasoro/Schwarzian correspondence, namely that the 2d bulk Virasoro constraints are equivalent to the graviton equation of motion of the 1d boundary theory, at least, on the SL(2, R) invariant vacuum
As an indication of physics of near-extremal black holes, the JT model, for example, captures the first order correction κ−1T to the entropy of near extremal black holes, S(T ) = S0 + κ−1T + O(T 2), where S0 is the entropy of extremal black holes and κ is the energy scale of symmetry breaking [8, 11, 12]
It has been known that the quantum CGHS (qCGHS) model has an exact AdS2 vacuum with a constant dilaton [32]
Summary
The CGHS model [1] is a model of 2d dilaton gravity which arises as the effective twodimensional theory of extremal dilatonic black holes in four and higher dimensions [34–39] and is defined by the action. The matter fields fi originate from Ramond-Ramond fields in type II superstring theories This model has been extensively studied in the early 90’s as a model of evaporating black holes. The model is classically solvable and has a simple eternal black hole solution in an asymptotically flat and linear dilaton spacetime. The equations of motion for the Liouville field ρ, dilaton φ and matter fields fi are given, respectively, by 0 = T+− = e−2φ(2∂+∂−φ − 4∂+φ∂−φ − λ2e2ρ) − N ∂+∂−ρ , 12. This system is subjected to the Virasoro constraints, i.e. the equations of motion for g±±:.
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