$AdS_2$ holography is (non-)trivial for (non-)constant dilaton

Understand

We study generic two-dimensional dilaton gravity with a Maxwell field and prove its triviality for constant dilaton boundary conditions, despite of the appearance of a Virasoro algebra with non-zero central charge.

• We do this by calculating the canonical boundary charges, which turn out to be trivial, and by calculating the quantum gravity partition function, which turns out to be unity.
• We show that none of the following modifications changes our conclusions: looser boundary conditions, non-linear interactions of the Maxwell field with the dilaton, inclusion of higher spin fields, inclusion of generic gauge fields.
• Finally, we consider specifically the charged Jackiw--Teitelboim model, whose holographic study was pioneered by Hartman and Strominger, and show that it is non-trivial for certain linear dilaton boundary conditions.