Holography for asymptotically locally Lifshitz spacetimes

TL;DR

This paper defines and constructs asymptotically locally Lifshitz spacetimes, establishing boundary conditions, dual field theory sources, and a holographic renormalization procedure to compute one-point functions with arbitrary sources.

Contribution

It introduces a new framework for asymptotically locally Lifshitz spacetimes, including boundary conditions, dual operators, and a holographic renormalization method.

Findings

Constructed solutions with asymptotic expansion

Identified boundary data as sources for dual operators

Developed holographic renormalization for Lifshitz spacetimes

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.