Holographic geometry for non-relativistic systems emerging from generalized flow equations

An intriguing result presented by two of the present authors is that an anti de Sitter space can be derived from a conformal field theory by considering a flow equation. A natural expectation is that given a certain data on the boundary system, the associated geometry would be able to emerge from a flow, even beyond the conformal case. As a step along this line, we examine this scenario for non-relativistic systems with anisotropic scaling symmetries, such as Lifshitz field theories and Schr\"odinger invariant theories. In consequence we obtain a new hybrid geometry of Lifshitz and Schr\"odinger spacetimes as a general holographic geometry in this framework. We confirm that this geometry reduces to each of them by considering special non-relativistic models.