Holographic Renormalization for z=2 Lifshitz Space-Times from AdS

TL;DR

This paper develops a holographic renormalization framework for z=2 Lifshitz space-times by reducing from AdS solutions, revealing two distinct anomalies and connecting to Horava-Lifshitz gravity.

Contribution

It introduces a method to perform holographic renormalization for z=2 Lifshitz space-times via dimensional reduction from AdS, characterizing boundary data and anomalies.

Findings

Identifies two separate anomalies with their own central charges.

Establishes a connection between Lifshitz anomalies and AdS conformal anomaly.

Derives a Horava-Lifshitz type action with a nonzero potential for z=2 gravity.

Abstract

Lifshitz space-times with critical exponent z=2 can be obtained by dimensional reduction of Schroedinger space-times with critical exponent z=0. The latter space-times are asymptotically AdS solutions of AdS gravity coupled to an axion-dilaton system and can be uplifted to solutions of type IIB supergravity. This basic observation is used to perform holographic renormalization for 4-dimensional asymptotically z=2 locally Lifshitz space-times by Scherk-Schwarz dimensional reduction of the corresponding problem of holographic renormalization for 5-dimensional asymptotically locally AdS space-times coupled to an axion-dilaton system. We can thus define and characterize a 4-dimensional asymptotically locally z=2 Lifshitz space-time in terms of 5-dimensional AdS boundary data. In this setup the 4-dimensional structure of the Fefferman-Graham expansion and the structure of the counterterm action, including the scale anomaly, will be discussed. We find that for asymptotically locally z=2 Lifshitz space-times obtained in this way there are two anomalies each with their own associated nonzero central charge. Both anomalies follow from the Scherk--Schwarz dimensional reduction of the 5-dimensional conformal anomaly of AdS gravity coupled to an axion-dilaton system. Together they make up an action that is of the Horava-Lifshitz type with nonzero potential term for z=2 conformal gravity.