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We study the gravitational edge mode of the Jackiw-Teitelboim (JT) gravityand the constrained $sl(2,\mathbb{R})$ BF theory for the asymptoticallyAdS$_2$. We revisit the derivation of the Schwarzian theory from the wigglingboundary as an action for the gravitational edge mode. We present analternative description for the gravitational edge mode from the metricfluctuation with the fixed boundary, which is also known as the would-be gaugemode in the gravity. We clarify the relation between the wiggling boundary andthe would-be gauge mode. We demonstrate a natural top-down derivation of$PSL(2,\mathbb{R})$ gauging and the path integral measure of the Schwarziantheory. In the constrained $sl(2,\mathbb{R})$ BF theory, we develop a methodfor incorporating the gravitational edge mode in the BF theory. In this BFtheory coupled to the edge mode, we derive the Schwarzian theory with$PSL(2,\mathbb{R})$ gauging. We show that the Haar measure for the Iwasawadecomposition of $PSL(2,\mathbb{R})$ leads to the path integral measure.

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