The quantum gravity dynamics of near extremal black holes

An explicit illustration of this fact is given in Appendix C of Yang (2019) for a massless scalar field.

“An explicit illustration of this fact is given in Appendix C of Yang (2019), for the case of a massless scalar field with (actually the calculation applies to any two-dimensional conformal field theory).22”

Using the known propagator of the particle in the magnetic field in the same limit, one can derive a suggestive expression for JT boundary correlators for ordered operators.

“Using the known propagator of the particle in the magnetic field in the same limit, one can derive the following suggestive expression for JT boundary correlators for the simplest case of ordered operators (Yang 2019):3.85where the ingredients are the bulk propagators of the particle in magnetic field model in proper time (between points in the hyperbolic disk and ) and the “undressed” bulk matter”

The GHY boundary term of the gravity path integral can be rewritten using the 2d Gauss-Bonnet theorem into a worldline path integral, which is a non-relativistic particle in 2d hyperbolic space in an imaginary infinite magnetic field.

“A different approach uses a direct rewriting of the GHY boundary term of the gravity path integral using the 2d Gauss–Bonnet theorem into a worldline path integral as (Kitaev and Suh 2019; Yang 2019; Suh 2020):3.83which is a non-relativistic particle in 2d hyperbolic space (T, Z) in an imaginary infinite magnetic field.”