Aspects of two-dimensional dilaton gravity, dimensional reduction, and holography

We discuss aspects of generic two-dimensional dilaton gravity theories. The two-dimensional geometry is in general conformal to the two-dimensional anti–de Sitter space ( AdS2) 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 two-dimensional description dovetails with the higher dimensional one. We also discuss more general theories containing an extra scalar field which now drives nontrivial dynamics. Finally we discuss aspects of the two-dimensional cosmological singularities discussed in earlier work. These studies suggest that generic two-dimensional dilaton gravity theories are somewhat distinct from Jackiw-Teitelboim (JT) gravity and theories "near JT".