Trace anomaly and Hawking effect in 2D dilaton gravity theories

These notes summarize the content of two of our papers dealing with two-dimensional (2D) dilaton gravity theories [1,2]. Our presentation in Santa Margherita was essentially based on the first paper [1], whereas the content of the second one [2] was briefly sketched as work in progress. For sake of completeness it seems to us advisable to give a full account of the recent results of Ref. [2] in these notes. 2D dilaton gravity theories have become very popular in recent years. They represent simple toy models for studying 4D black hole physics and its related challenging issues such us the ultimate fate of black holes or the loss of quantum coherence in the evaporation process. Moreover, the relation with non-critical string theory and the renormalizability of gravity in two space-time dimensions give to these theories an intrinsic interest, which goes beyond black hole physics. Even though 2D dilaton gravity contains, as particular cases, models with different features (e.g. the Callan-GiddingsHarvey-Strominger (CGHS) model [3], the JackiwTeitelboim (JT) model [4]), a simple, unified description of the general theory still exists. In this paper we will discuss three crucial issues of 2D dilaton gravity, which, as we shall see, are deeply interconnected. These issues are the equivalence of 2D dilaton gravity models under Weyl rescalings