Nearly AdS$_2$ holography in quantum CGHS model

Understand

In light of recent developments in nearly AdS$_2$ 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$_2$ 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 AdS$_2$ vacuum nearly AdS$_2$.