Gravitational Edge Mode in Asymptotically AdS$_2$: JT Gravity Revisited

Understand

We study the gravitational edge mode of the Jackiw-Teitelboim (JT) gravity and its $sl(2,\mathbb{R})$ BF theory description with the asymptotic AdS$_2$ boundary condition.

• We revisit the derivation of the Schwarzian theory from the wiggling boundary as an action for the gravitational edge mode.
• We present an alternative description for the gravitational edge mode from the metric fluctuation with the fixed boundary, which is often referred as "would-be gauge mode".
• We clarify the relation between the wiggling boundary and the would-be gauge mode.