  We classify and study defects in 2d Jackiw-Teitelboim gravity. We show these
are holographically described by a deformation of the Schwarzian theory where
the reparametrization mode is integrated over different coadjoint orbits of the
Virasoro group. We show that the quantization of each coadjoint orbit is
connected to 2d Liouville CFT between branes with insertions of Verlinde loop
operators. We also propose an interpretation for the exceptional orbits. We use
this perspective to solve these deformations of the Schwarzian theory,
computing their partition function and correlators. In the process, we define
two geometric observables: the horizon area operator $\Phi_h$ and the geodesic
length operator $L(\gamma)$. We show this procedure is structurally related to
the deformation of the particle-on-a-group quantum mechanics by the addition of
a chemical potential. As an example, we solve the low-energy theory of complex
SYK with a U(1) symmetry and generalize to the non-abelian case.
