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

Understand

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.