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

TL;DR

This paper explores the properties of 2D dilaton gravity, including holographic aspects, regularization of IR singularities, and connections to higher-dimensional theories, highlighting differences from JT gravity.

Contribution

It provides a comprehensive analysis of generic 2D dilaton gravity, including holographic renormalization, dimensional reduction links, and the role of additional scalar fields.

Findings

IR singularities can be regulated by black holes.

Holographic energy-momentum tensor requires counterterms.

2D theories differ from JT gravity and near-JT models.

Abstract

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. We also discuss more general theories containing an extra scalar field which now drives nontrivial dynamics. Finally we discuss aspects of the 2-dimensional cosmological singularities discussed in earlier work. These studies suggest that generic 2-dim dilaton gravity theories are somewhat distinct from JT gravity and theories "near JT".