Joshua Kames-King (Bonn): Deformations of JT Gravity and KdV Equations

Recently, it was shown that the duality of double-scaled matrix models and JT gravity can be extended to include surfaces with conical defects.
We show that the thermal partition function of this deformed theory may be written as the free energy of topological gravity around a shifted expansion point.
By use of the KdV equation we furnish an off-shell description for both the single and multi-boundary cases of the partition function.
We also rewrite the deformed partition function as a low temperature expansion, which allows for a convenient calculation of contributions up to a desired order.
We use this approach to demonstrate the existence of a Hawking-Page phase transition between connected and disconnected surfaces for this instance of JT gravity.
Furthermore, we calculate the spectral form factor and compare with the standard JT case.
We conclude by commenting on the dS2 case.