On aspects of 2-dim dilaton gravity, dimensional reduction and holography

Understand

We discuss aspects of generic 2-dimensional dilaton gravity theories.

• The 2-dim geometry is in general conformal to $AdS_2$ and has IR curvature singularities at zero temperature: this can be regulated by a black hole.
• The on-shell action is divergent: we discuss the holographic energy-momentum tensor by adding appropriate counterterms.
• For theories obtained by dimensional reduction of the gravitational sector of higher dimensional theories, for instance higher dimensional $AdS$ gravity as a concrete example, the 2-dimensional description dovetails with the higher dimensional one.