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

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

2011-07-18

arxiv.org/abs/1107.3345v2

Physics

High Energy Physics

High Energy Physics - Phenomenology

10 pages; added reference and discussion, this version to appear in PRD

Scientific paper

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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