Restoration of Lorentz Symmetry for Lifshitz-Type Scalar Theory

Abstract

The purpose of this paper is to present our study on the restoration of the Lorentz symmetry for a Lifshitz-type scalar theory in the infrared region by using nonperturbative methods. We apply the Wegner-Houghton equation, which is one of the exact renormalization group equations, to the Lifshitz-type theory. Analyzing the equation for a z=2, d=3+1 Lifshitz-type scalar model, and using some variable transformations, we found that broken symmetry terms vanish in the infrared region. This shows that the Lifshitz-type scalar model dynamically restores the Lorentz symmetry at low energy. Our result provides a definition of ultraviolet complete renormalizable scalar field theories. These theories can have nontrivial interaction terms of ϕ^{n} (n=4, 6, 8, 10) even when the Lorentz symmetry is restored at low energy.

24 pages, 7 figures; v2: minor corrections, added references; v3: added comments on the initial conditions in section 4, typos corrected, published version