Lifshitz theories with extra dimensions and 3+1-d Lorentz invariance

TL;DR

This paper develops Lifshitz scalar field theories in 4+1 dimensions that preserve 3+1-dimensional Lorentz invariance, potentially enabling ultraviolet completions of extra-dimensional theories with improved renormalizability.

Contribution

It introduces a novel construction of Lifshitz theories with extra dimensions that maintain 3+1-d Lorentz invariance and shows how increasing derivative order enhances renormalizability.

Findings

Lambda phi^4 theory becomes less non-renormalisable as n increases

Infinite-n limit may lead to a UV-complete non-local theory

Preserves 3+1-d Lorentz invariance in higher-dimensional Lifshitz theories

Abstract

We construct Lifshitz scalar field theories in 4+1 dimensions which retain 3+1-d Lorentz invariance and therefore ensure a unique limiting speed in the 3+1-d world. Such a construction is potentially useful in developing field-theoretic ultraviolet completions of extra-dimensional field theories. The extra dimension y is treated asymmetrically from the usual three spatial dimensions by introducing derivatives of order 2n with respect to y in the action. We show that lambda phi^4 theory becomes progressively less non-renormalisable by power counting as n is increased. This suggests that the non-local theory obtained in the infinite-n limit may be complete in the ultraviolet.