Aspects of Holography in Two-Dimensional Dilaton Gravity
The simplest toy models for classical and quantum gravity that can have black hole solutions are two-dimensional. Yet, two-dimensional Einstein gravity is not among them: in two dimensions the Einstein tensor vanishes identically. Dilaton gravity, however, is a consistent theory of gravity in two dimensions. However, holography in two dimensions appears to be, in some aspects, more subtle than its higher-dimensional relative. Following an introduction to two-dimensional dilaton gravity and its formulation as a Poisson sigma model, I will describe the holographic renormalization of different dilaton gravity models and discuss different set-ups for AdS2 holography.