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Abstract: We provide a framework for non-relativistic holography so that a covariantaction principle ensuring the Galilean symmetry for dual conformal field theoryis given. This framework is based on the Bargmann lift of the Newton-Cartangravity to the one-dimensional higher Einstein gravity, or reversely, thenull-like Kaluza-Klein reduction. We reproduce the previous zero temperatureresults, and our framework provides a natural explanation about why theholography is co-dimension 2. We then construct the black hole solution dual tothe thermal CFT, and find the horizon is curvature singular. However, we areable to derive the sensible thermodynamics for the dual non-relativistic CFTwith correct thermodynamical relations. Besides, our construction admits a nullKilling vector in the bulk such that the Galilean symmetry is preserved underthe holographic RG flow. Finally, we evaluate the viscosity and find it zero ifwe neglect the back reaction of the singular horizon, otherwise, it could benonzero.

Autor: Feng-Li Lin, Shang-Yu Wu


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