Abstract
We search a gravitational system which allows a non-relativistic hybrid geometry interpolating the Schr\"odinger and Lifshitz spacetimes as a solution, as a continuation of the previous work employing a flow equation. As such a candidate an Einstein-Maxwell-Higgs system naturally arises and we verify that this system indeed supports the hybrid geometry with the help of a gauge-fixing term for diffeomorphism. As a result, this gravitational system may be interpreted as a holographic dual of a general non-relativistic system at the boundary.
Highlights
It is a new paradigm to realize quantum theory of gravity as a hologram of a quantum field theory at boundary [1,2] and has attracted much interest since the discovery of the AdS/CFT correspondence [3], which admits nontrivial tests by explicit computation [4,5]
The purpose of this letter is to fill this gap, and to stress that the flow equation method works for the matter sector as well, not restricted to the metric
This result strongly indicates that the flow equation method can capture gravitation beyond geometry
Summary
It is a new paradigm to realize quantum theory of gravity as a hologram of a quantum field theory at boundary [1,2] and has attracted much interest since the discovery of the AdS/CFT correspondence [3], which admits nontrivial tests by explicit computation [4,5]. At a general point in the parameter space, this metric describes a d-dimensional Lifshitz space-time with the dynamical critical exponent 2 times a straight line, while it enhances to the Schrödinger space-time in d + 1 dimensions when β = γ = 0. This geometry would deserve to be called an NR hybrid geometry. The purpose of this letter is to fill this gap, and to stress that the flow equation method works for the matter sector as well, not restricted to the metric. This result strongly indicates that the flow equation method can capture gravitation beyond geometry
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