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arXiv · 1107.3345

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

Xiao-Gang He·Sandy S. C. Law·Raymond R. Volkas
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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.

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Xiao-Gang He, Sandy S. C. Law, Raymond R. Volkas. 2011-07-18. Lifshitz theories with extra dimensions and 3+1-d Lorentz invariance. https://doi.org/10.1103/physrevd.84.125017

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