Holographic geometry for nonrelativistic systems emerging from generalized flow equations

Abstract

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 nonrelativistic systems with anisotropic scaling symmetries, such as Lifshitz field theories and Schrödinger invariant theories. In consequence we obtain a new hybrid geometry of Lifshitz and Schrödinger spacetimes as a general holographic geometry in this framework. We confirm that this geometry reduces to each of them by considering special nonrelativistic models.