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arXiv · 1803.06827

$AdS_2$ dilaton gravity from reductions of some nonrelativistic theories

Kedar S. Kolekar·K. Narayan
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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.

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Kedar S. Kolekar, K. Narayan. 2018-03-19. $AdS_2$ dilaton gravity from reductions of some nonrelativistic theories. https://doi.org/10.1103/physrevd.98.046012

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