AdS2 dilaton gravity from reductions of some nonrelativistic theories

We study dilaton-gravity theories in two dimensions obtained by dimensional reduction of higher-dimensional nonrelativistic theories. Focusing on certain families of extremal charged hyperscaling violating Lifshitz black branes in Einstein-Maxwell-scalar theories with an extra gauge field in four dimensions, we obtain AdS(2) backgrounds in the near-horizon throats. We argue that these backgrounds can be obtained in equivalent theories of two-dimensional 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.