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

TL;DR

The paper investigates generic two-dimensional dilaton gravity theories, especially those arising from dimensional reduction of higher-dimensional AdS gravity, showing that their 2D geometries are typically conformal to $AdS_2$ and harbor IR curvature singularities at zero temperature that can be regulated by a black hole. It develops a holographic renormalization framework to address UV divergences of the on-shell action and demonstrates that the 2D holographic stress tensor matches the higher-dimensional description upon reduction, thereby linking the 2D theory to its UV-complete higher-dimensional origin. The work also analyzes low-lying soft modes, finds departures from the $nAdS_2$ Schwarzian, and explores the role of an additional scalar $\Psi$, including its impact on cosmological singularities and scalar-probe correlators, which show operator dimensions $\Delta = 2$ (for $d_i=2$) and generally $\Delta = 1 + {d_i\over 2}$, with correlators insensitive to the zero-temperature singularity. Overall, the results suggest that generic 2D dilaton gravities are qualitatively distinct from JT gravity and may provide an effective holographic framework with ensemble-like features for higher-dimensional gravity, rather than a strict JT-like duality.

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".