Nearly AdS holography in quantum CGHS model
arXiv:1910.12542 · doi:10.1007/JHEP01(2020)178
Abstract
In light of recent developments in nearly AdS holography, we revisit the semi-classical version of two-dimensional dilaton gravity proposed by Callan, Giddings, Harvey, and Strominger (CGHS) in the early 90's. In distinction to the classical model, the quantum corrected CGHS model has an AdS vacuum with a constant dilaton. By turning on a non-normalizable mode of the Liouville field, i.e. the conformal mode of the gravity, the explicit breaking of the scale invariance renders the AdS vacuum nearly AdS. 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 AdS 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 bulk Virasoro constraints are equivalent to the graviton equation of motion of the boundary theory, at least, on the invariant vacuum.
arXiv comment25 pages, an error corrected and reference added
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