Power counting renormalizability of scalar theory in Lifshitz spacetime

TL;DR

This paper investigates the renormalizability of scalar field theories in Lifshitz spacetime, analyzing spectral dimensions, and discusses implications for quantum gravity and holography.

Contribution

It provides a detailed power counting analysis of scalar theories in Lifshitz spacetime, including spectral dimension calculations and insights into holographic dualities.

Findings

Spectral dimension becomes 2 + (D/z) after radion integration

Flowing into AdS spacetime can avoid Lifshitz singularities

Implications for quantum gravity in Lifshitz backgrounds

Abstract

We analyse the power counting renormalizability of scalar theory in Lifshitz spacetime in D+2 dimensions. We show the spectral dimension becomes 2+(D/z) (z is the critical exponent) after integrating out the radion field. We comment on the AdS/CFT correspondence, and on how to avoid the Lifshitz singularity by flowing into AdS spacetime in the infrared. We also comment on the quantum gravity in Lifshitz spacetime.