Lifshitz Space-Times for Schroedinger Holography

TL;DR

The paper demonstrates that asymptotically locally Lifshitz spacetimes are holographically dual to field theories with Schroedinger invariance by carefully matching bulk sources to torsional Newton–Cartan geometry on the boundary and constructing a gauge-invariant boundary energy–momentum tensor and mass current. It shows that the sources and vevs transform covariantly under the Schroedinger algebra and that their Ward identities are organized accordingly, even when the energy flux appears to be marginal for $z>1$. Using the Einstein–Proca–Dilaton framework, it provides a concrete holographic setup that yields a TTNC/TNC boundary geometry and a gauged Schrödinger structure. These results lay a foundation for non-relativistic holography and point toward hydrodynamic and generalized symmetry extensions, including charged cases and potential Schrodinger–Virasoro enhancements.

Abstract

We show that asymptotically locally Lifshitz space-times are holographically dual to field theories that exhibit Schroedinger invariance. This involves a complete identification of the sources, which describe torsional Newton-Cartan geometry on the boundary and transform under the Schroedinger algebra. We furthermore identify the dual vevs from which we define and construct the boundary energy-momentum tensor and mass current and show that these obey Ward identities that are organized by the Schroedinger algebra. We also point out that even though the energy flux has scaling dimension larger than z+2, it can be expressed in terms of computable vev/source pairs.