Holographic boundary conformal field theories have recently played an important role in the study of the black hole information paradox. In a particular duality frame they describe a matter CFT whose excitations can move between a non-gravitating region (the bath) and a gravitating region. In yet another, so called doubly-holographic, description one usually considers an AdS3 spacetime in which an end-of-the-world (ETW) brane is introduced, whose action is given by JT gravity.
In this talk I will explain that, quite generally, deformations of 2d ETW branes are controlled by a particular dilaton gravity theory coupled to a large-c, effective CFT. This dilaton gravity theory is related to Liouville Theory and reduces to AdS-, dS-, and flat-JT gravity in various limits of the branes' tension and at large central charge. Using the bulk picture of double holography, this perspective allows to derive the correct area functional for extremal surfaces in the presence of JT gravity on the brane. Adding JT to the ETW brane is equivalent to infinitesimal deformations of the BCFT boundary and seems to capture universal effects of boundary deformations, possibly even for non-holographic theories.