HOLOTUBE: JT gravity with defects and the Aharonov-Bohm effect

Jackiw-Teitelboim (JT) gravity is remarkable, especially when it is defined on Euclidean negatively curved backgrounds. There is a strong evidence that if its partition function is defined as sum over all higher genus topologies, the dual theory of JT gravity is a random ensemble of some quantum mechanical systems rather than a specific theory. This is a “new” type of AdS/CFT correspondence, which is analogous to the “old” c=1 matrix/2d string duality.
We study JT gravity with generalized dilaton potential on Euclidean two-dimensional negatively curved backgrounds. The effect of the generalized dilaton potential is to induce a conical defect on the two-dimensional 
manifolds. We show that this theory can be written as the ordinary quantum mechanics of a charged particle on a hyperbolic disk in the presence of a constant background magnetic field plus a pure gauge Aharonov-Bohm field. This picture allows us to exactly evaluate the corresponding dynamical gravitational degrees of freedom.