Holography for asymptotically locally Lifshitz spacetimes

TL;DR

Problem: extend holographic duality to Lifshitz-like non-relativistic boundary theories with a robust dictionary. Approach: define asymptotically locally Lifshitz spacetimes via frame fields, analyze the massive-vector bulk theory, and develop a dilatation-based holographic renormalization framework. Key results: for $z<2$, asymptotically locally Lifshitz solutions exist for arbitrary boundary data; for $z\ge2$, sources for irrelevant operators must be set to zero (with potential changes in boundary conditions for $z>4$); divergences are removable by local counterterms, yielding finite stress-tensor vevs. Significance: enables controlled holographic computation of non-relativistic boundary correlators on curved backgrounds and clarifies the Lifshitz holographic dictionary and renormalization structure.

Abstract

We give a definition of asymptotically locally Lifshitz spacetimes, with boundary data appropriate for a non-relativistic theory on the boundary. Solutions satisfying these boundary conditions are constructed in an asymptotic expansion. We identify the boundary data with sources for dual field theory operators, and give a prescription for calculating the one-point functions of the field theory operators (including the stress tensor) in the presence of arbitrary sources. The divergences in these one-point functions can be cancelled by holographic renormalization, adding counterterms which are local functions of the boundary data.