$AdS_2$ dilaton gravity from reductions of some nonrelativistic theories

TL;DR

This work shows how $AdS_2$ dilaton gravity arises in two dimensions by dimensional reduction of higher-dimensional nonrelativistic backgrounds, notably charged hvLif black branes. The near-horizon extremal geometries yield $AdS_2$ throats described by a 2D dilaton-gravity theory with an extra scalar; linearized fluctuations reproduce a universal Schwarzian boundary action whose coefficient is set by the extremal entropy, linking to JT gravity and SYK-like physics. The authors analyze perturbations and demonstrate stability for physically allowed $(z,\theta)$, and they extend the analysis to relativistic limits and null reductions, showing the Schwarzian structure persists as a universal descriptor of near-extremal dynamics. The results clarify how the extra scalar and dilaton interact in 2D after reduction and suggest a broader landscape of $AdS_2$ theories with potential 1D dual interpretations.

Abstract

We study dilaton-gravity theories in 2-dimensions obtained by dimensional reduction of higher dimensional nonrelativistic theories. Focussing on certain families of extremal charged hyperscaling violating Lifshitz black branes in Einstein-Maxwell-scalar theories with an extra gauge field in 4-dimensions, we obtain $AdS_2$ backgrounds in the near horizon throats. We argue that these backgrounds can be obtained in equivalent theories of 2-dim dilaton-gravity with an extra scalar, descending from the higher dimensional scalar, and an interaction potential with the dilaton. A simple subcase here is the relativistic black brane in Einstein-Maxwell theory. We then study linearized fluctuations of the metric, dilaton and the extra scalar about these $AdS_2$ backgrounds. The coefficient of the leading Schwarzian derivative term is proportional to the entropy of the (compactified) extremal black branes.